Period of a Pendulum:
The period of a pendulum is dependent on the length of it and the acceleration due to gravity. Since it is directly related, as the length of the pendulum increases, the period also increases. Although, if the gravitational field strength increases, that means the period will decrease. The pendulum’s period does not depend on the displacement or the mass. Increasing the amplitude means that there is a larger distance to travel, but the restoring force also increases, which proportionally increases the acceleration. This means the mass can travel a greater distance at a greater speed. These attributes cancel each other, which means the amplitude has no effect on period. The pendulum’s inertia resists the change in direction, but it’s also the source of the restoring force. As a result, the mass cancels out too. |
Period of a Spring:
The period of a spring is dependent on its mass and its spring constant. Since they are directly related, when the mass increases, the period also increases. Although, if the spring constant increases, that means the period will decrease. The spring's period does not depend on the amplitude. Increasing the amplitude means the mass travels more distance for one cycle. However, increasing the amplitude also increases the restoring force. The increase in force proportionally increases the acceleration of the mass, so the mass moves through a greater distance in the same amount of time. Thus, increasing the amplitude has no net effect on the period of the oscillation. |
The maximum and minimum values of displacement are when the velocity is equal to 0 because that is when the object is moving back towards the equilibrium. Furthermore, the maximum value for velocity is seen when displacement is 0 because that is when the object has its highest kinetic energy, and hence its highest velocity.
The more complicated part is the acceleration vs time graph. It is essentially the position vs time flipped over the x axis. This is because the restoring force is proportional to the displacement, and hence, the restoring force goes in the opposite direction of the displacement. Eventually, the net force will try to pull the object back to its equilibrium. |
https://www.khanacademy.org/science/ap-physics-1/simple-harmonic-motion-ap/introduction-to-simple-harmonic-motion-ap/a/introduction-to-simple-harmonic-motion-review
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