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### Damped forced Oscillation with variable external frequency

Consider that we have the following forced vibration with an input frequency $ω(t)$ variable in time. $$m\ddot{x}+c\dot{x}+kx = F_0 \sin{(\omega(t) t)}$$ Assuming that the solution must be a ...
128 views

### Harmonic motion with friction [closed]

Consider an undamped mass and spring system with friction. The friction is not proportional to the velocity of the mass. If we solve the corresponding differential equation,the spring will oscillate ...
76 views

### Explanation of a spring using “Artistotle's law of motion”, $\vec{F}=m\vec{v}$

So I was watching Susskind's Classical Mechanics lectures and I didn't understand something in the second lecture. He was telling about Aristotle's Law of motion which is $$\vec F = m\vec v.$$ He ...
43 views

### Potential gravitational energy versus potential spring energy [duplicate]

My textbook points out the following predicament, and I do not know the answer, despite a lot of thinking: A spring is hanging of a ceiling and a mass is attached. As a result the spring descends to ...
47 views

### Phase shift of damped mass on spring with moving source [closed]

I have a setup with a moving (upwards, downwards) board on which there is a spring mounted on the edge. The spring has a mass $m$ on its end and is damped in some sort of liquid. What methods could I ...
4k views

### Finding the damping constant and period from looking at a graph [closed]

I want to make sure there are no holes in my logic in solving this problem. From the figure, I am instructed to determine the damping constant as accurately as possible. Here's what my thought ...
100 views

### Deterministic non-harmonic motion of a single spring

Is there anything describing a spring's motion when e.g pulled and released, or pushed and released, with no mass-body attached to the spring. I.e not your usual "mass motion on a spring"-equation. I'...
210 views

### Determination of spring constant $k$ for an elastomer

Primary Question: How can you determine the spring constant $k$ of an elastic material? I was recently tasked with finding the spring constant for a series of elastomeric materials, the first of ...
If a spring is stretched by a weight of mass m, (so the extension is $\Delta x$) then $k = \frac W{\Delta x} = \frac {mg}{\Delta x}$. So $k\Delta x= mg$. When the Spring is stretched by distance \$\...