# Tagged Questions

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### Why do we use sine/cosines in Simple Harmonic Motion? [duplicate]

For example, to calculate the displacement of the particle in an harmonic oscillator we do: $$x(t) = x_{\max} \cos(ωt+φ)$$ What do we find out taking the cosine of (ωt+φ)? Example Graph:
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### Rational ratio of frequencies leads to isolating integral of motion

Padmanabhan's discussion of dynamics mentions that in general the two dimensional harmonic oscillator fills the surface of a two torus. He further notes that there will be an extra isolating integral ...
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### Deriving spring oscilation period [duplicate]

We have a spring attached to a wall and at the other part an object on a frictionless surface. I tried to calculate the spring oscilation period. I used the conservation of energy and kinematics ...
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### Finding the minimum radius of the pivoted disc

Here is a question based on Simple Harmonic Motion that I tackled just now. However I think I am having an approach to tackle this but I am not sure about it. Ouestion: A uniform disc of radius ...
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### Help explain how direction change relates to acceleration [duplicate]

I was doing some simple harmonic motion problems and I came across this picture describing the position, velocity and acceleration of a linear oscillator. At the moment in time when v is 0 the ...
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### Questions related to resonance/standing-waves and sound

I understand resonance for a simple harmonic oscillator but not for more complex systems like standing waves. How can I be in resonance with the normal mode in an organ pipe? I understand that the ...
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### Meaning of “Simple” in Simple Pendulum and Simple Harmonic Motion?

I have gone through the Phys.SE question Why is simple harmonic motion called so?. From the 1st answer of this Question it seems to me that another type of "Harmonic motion" is "Damped Harmonic ...
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### Faster than critical damping for harmonic oscillator?

The image below shows damping for spring oscillator with Hooke law F=-kx and damped with F=-cv where: k is spring constant x is oscillator position c is damping coefficient v is velocity of oscillator ...
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### A block falling from a height on a block suspended by spring [closed]

The block suspended by the spring is hanging freely and its mass is M. The small block of mass m is dropped on the bigger block from height h. After the small block is dropped 》》》 I want help in ...
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### Double-spring mass system

We just had a lesson about elementary mass-spring systems (SHO), and I thought about a horizontal situation with two springs with the test mass oscillating in between. If we are to manually stretch ...
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### Moment of inertia of a system in different cases

A rod of mass $m$ and length $l$ is pivoted at one end to ceiling and free to rotate in the vertical plane. A disc of radius $R$, which is less than $l$, can be fixed at its other end in 2 ways : ...
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### Simple Harmonic Motion Question - Block on Platform [closed]

A platform is executing SHM in a vertical direction with an amplitude of $5$ cm and a frequency of $\frac{10}{\pi}$ vibrations per second. A block is placed on the platform at the lowest point of its ...
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### Difference between the two equations for acceleration

I came upon this while studying S.H.M. Well,is there a difference between writing $$a=\frac{dv}{dt}\;$$ and $$a=v\frac{dv}{dx}\;$$ do they differ on the basis of one being a vector and the other ...
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A potential given by : $$V(x,y,z) = \frac{1}{2}m(x^2+y^2+\frac{z^2}{2}).$$ Which component of angular momentum is conserved. An attempt: Angular momentum along z, $L_{z} = m(x\dot{y} - ... 2answers 145 views ### Velocity and acceleration in SHM Can velocity and acceleration reach maximal values during the SHM simultaneously? Can you explain why? 1answer 238 views ### Simple pendulum. quick question [closed] I was trying to find an equation to find$T$and$\omega$for a simple pendulum when in an elevator while the elevator is accelerating. One scenario is when it accelerates in the positive up ... 1answer 525 views ### Equations of motion for a pendulum in 3D? I am trying to solve for the equations of motion to simulate a pendulum. I decided to use the spherical coordinates. The Lagrange equation is: where L = length of the rope ϕ= angle of the ... 1answer 168 views ### Period of small oscillations [duplicate] A light elastic string is stretched between two points, one lying vertically below the other. A particle is attached to the mid-point of the string, causing it to sink a distance h. Assuming that ... 2answers 544 views ### Mass-spring system on an incline I am reviewing for an exam next week, and this is one of the questions I am stuck on. I have the mass-spring system above with spring constant$k$on a frictionless incline. I would like to find the ... 1answer 377 views ### Two-block system connected to a spring Say you have two blocks with masses$m_1$and$m_2$, where$m_1>m_2$. The smaller block sits atop the larger block. The larger block is connected to a spring, which is then connected to a wall a ... 1answer 152 views ### Finding the tangential force experienced by a bob of mass m on a simple pendulum via the gradient/nabla operator) The problem was posed as follows. Given a pendulum of length$L$with a mass$m$attached to it, which forms an angle$\theta$from the y-axis to the direction of swinging. First we had to find the ... 1answer 72 views ### Spring with changing equilibrium Suppose that we have two cars on a track, each with a different mass. Now suppose that the cars are connected with a spring. We smack one car. I would like to write down the equations of motion for ... 0answers 1k views ### Equations of motion for a pendulum and spring system The question is available here: I've modeled the building as a rod on a torsional spring (with a pendulum hanging from the top).$\phi$is the angle from the centre for the pendulum and$\theta$... 2answers 1k views ### Why doesn't mass of bob affect time period? Please correct me if I'm going wrong - By the gravitation formula:$F = \frac{G m_1 m_2}{r^2} $, So if the mass of a bob is greater then the torque on it should increase because the Force increased ... 2answers 691 views ### Energy transfer in a coupled pendulum If you take a look at this video you will see what kind of a coupled pendulum I'm talking about. So I made a similar one in my high school's physics lab, using light metal bobs(much lighter than the ... 2answers 90 views ### Is it possible to find a “replacement pendulum” for a system of two equal but perpendicular pendulums? I ask this question, because at the end of this long day I'm just too dazed to derive the proofs myself (even though I know that I should feel ashamed for this). So, the question: Given two ... 1answer 137 views ### Simple pendulum and planet mass [closed] A simple pendulum,$20cm$in length, has the period of$2.7s$on a certain planet. Find the mass of the planet if its diameter is$18000km$.$G=6.67\times10^{-11}Nm^2/kg^2 $I have no idea how to get ... 0answers 38 views ### Delivered/Reflected Power by Drive on a Hamiltonian System Imagine a SHO with a drive F(t). (or in general a Hamiltonian system) What is the power delivered to the system and can we talk about the power reflected? is i am imagining say a MW oscillator ... 0answers 805 views ### Effective mass in Spring-with-mass/mass system Suppose you have a particle of mass$m$fixed to a spring of mass$m_0$that, in turn, is fixed to some wall. I'm trying to calculate the effective mass$m'$that appears in the law of motion of the ... 1answer 1k views ### SHM of floating objects If we consider an object undergoing who has an acceleration proportional to the displacement of the object, it is going simple harmonic motion. In terms of Newton's second law, this is $$-\dfrac k ... 2answers 552 views ### Time period for spring connected body Two identical springs with spring constant k are connected to identical masses of mass M, as shown in the figures above. The ratio of the period for the springs connected in parallel (Figure 1) ... 1answer 703 views ### Pendulum in an elevator Suppose we have a pendulum tied to the ceiling of an elevator which is at rest. The pendulum is oscillating with a time period T, and it has an angular amplitude, say \beta. Now at some time ... 1answer 328 views ### Compound pendulum clarification? I read in a book the following about compound pendulum and small displacements: There are two points only for which the time period is minimum. there are maximum 4 points for which the time ... 0answers 37 views ### How can I find the frequency? [duplicate] Grocery stores often have spring scales in their produce department to weigh fruits and vegetables. The pan of one particular scale has a mass of 0.5 kg, and when you place a 0.5 kg sack of potatoes ... 2answers 171 views ### Potential energy during vertical fall Suppose I have a weightless spring connected perpendicularly to the ground, and it has on top of it some weightless surface. Now, I release some sticky object from height h above the system of light ... 1answer 391 views ### Simple harmonic oscillator system and changes in its total energy Suppose I have a body of mass M connected to a spring (which is connected to a vertical wall) with a stiffness coefficient of k on some frictionless surface. The body oscillates from point C to ... 3answers 3k views ### Can someone please derive T=2\pi\sqrt{l/g} or prove it without using calculus? I don't know much calculus, but I want to know that how one derives the formula to find time period T of a simple pendulum. 1answer 98 views ### Sitting on the bob of a pendulum Walter Lewin's best performance was the pendulum demonstration, and I copy the transcript now: Would the period come out to be the same or not? [students respond] Some of you think it's ... 3answers 6k views ### How to derive the period of spring pendulum? So I wanted to find out how to (simply, if that's possible) derive the formula for a period of spring pendulum: T=2\pi \sqrt{\frac{m}{k}}. However, Google doesn't help me here as all I see is the ... 1answer 411 views ### Writing equation for amplitude of driven harmonic oscillator in Lorentzian form This harmonic oscillator is driven and damped, with the form:$$\ddot{x} + \lambda \dot{x} + \omega_0^2 x = A \cos(\omega_d t)$$Now, I have used the ansatz (guess): x(t) = B \cos(\omega_d t + ... 2answers 250 views ### Understanding the concept of period of motion in simple harmonic motion formula I have a spring system, whose position equation is$$x(t) = c_1cos(8 \sqrt{2}t) + c_2sin(8 \sqrt{2}t)$$The textbook says it will have a period of motion of$\frac{2 \pi}{(8 \sqrt{2}t)}$. I ... 2answers 830 views ### Linear motion with variable acceleration Consider the following problem I pull a mass m resting at x = 0 on a frictionless table connected to a spring with some k by an amount A and let it go. What will be its speed at x=0? I know how to ... 2answers 174 views ### Force to use in harmonic oscillation through the inside of a planet I am to find an equation for the time it takes when one falls through a planet to the other side and returns to the starting point. I have seven different sets of values - mass of object falling, mass ... 2answers 4k views ### How to prove that a motion is Simple Harmonic Motion (SHM)? I would like to know how one could show and prove that a given motion is simple harmonic motion. Once given an answer, I'll apply that technique to an example I am trying to figure out. Thank you ... 1answer 207 views ### Simple Harmonic Motion. Why am I wrong? Why is my equation wrong more importantly? Problem/Solution ! I am deeply confused. B) We know that$x = 2\sin(3\pi t)$.$x' = 6\pi\cos(3\pi t)$So max speed is$6\pi6\pi = 6\pi \cos(3\pi t)\cos(3\pi t) = 13\pi t = ...
Consider a block of mass $m$ attached to a spring. Let it oscillate at a frequency $f$. Now each part of the spring is in SHM. so this means a wave is propagating through this spring.bCan this wave be ...