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I would like to know the forces acting on an SHM, and how they effect the motion. For example, take the motion of a simple pendulum as in the given image.Motion of a simple pendulum Which are the forces acting on this motion?

For simplicity, lets divide the motion into four parts, first one being the motion from the mean position(B) to the right extreme position(C), then back to B from C($2^{nd}$ part), then to A from B($3{rd}$ part) an finally the motion to B from A.

Now, which forces act on each parts and what they do to the motion (i.e, do they accelerate the motion or retard the motion etc)?

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  • $\begingroup$ Wording wise, forces don't "act on a motion". Forces act on objects, which influences their motion. $\endgroup$ – Aaron Stevens Aug 5 '18 at 1:32
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In simple harmonic motion, the mass always oscillates about a stable equilibrium point. The point B is the point of stable equilibrium in this system. This means that the forces would act in such a manner, that the mass would always have a tendency to move to point B, if it is slightly displaced from that point.

If it is moving from point B to C or from point B to A, the forces would be retarding and from A to B or C to B, they would be accelerating.

The only force that would cause any kind of acceleration(change in the speed of the mass) would be gravity. Tension is always at a right angle to the velocity, it would change the direction of its velocity but never its magnitude.

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  • $\begingroup$ What are the forces acting here? $\endgroup$ – RogUE Mar 14 '15 at 6:15
  • $\begingroup$ That would be 'tension' due to the string and 'gravity'. Consider a component of gravity that is perpendicular to the string. As the mass travels from mean to extreme, this component would always oppose the motion. And it would accelerate the mass when it moves from the extreme point to the mean point. $\endgroup$ – Sai Mar 14 '15 at 6:20
  • $\begingroup$ What would "tesion" do in each part of motion(retard or accelerate)? $\endgroup$ – RogUE Mar 14 '15 at 6:23
  • $\begingroup$ Tension is the force which helps the mass move in a circular path. It would always be perpendicular to the motion of the mass. It would neither be a cause for acceleration nor for retardation. $\endgroup$ – Sai Mar 14 '15 at 6:26
  • $\begingroup$ "Consider a component of gravity that is perpendicular to the string. As the mass travels from mean to extreme, this component would always oppose the motion. And it would accelerate the mass when it moves from the extreme point to the mean point", that is inertia is responsible for the motion from the mean point? $\endgroup$ – RogUE Mar 14 '15 at 6:40
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Weight and Tension in the string are two important things to consider here. I can select my half-cone angle as $\theta$. Then, the tension T is balanced by the cosine component of weight i.e m $\times$ g and the $\sin\theta$ component is the one directed towards mean position. If the angle is small, we can approximate $\sin \theta \sim \theta$. And you get a force which is directed towards mean [negative sign] and proportional to displacement, which means it is example of SHM.

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