Question

How can we find the amplitude and period of some SHM when the maximum acceleration and maximum velocity is given?

Answer 1

To find the amplitude and period of simple harmonic motion (SHM) when the maximum acceleration and maximum velocity are given, you can use the following equations:

1. Amplitude (A): The amplitude of SHM can be calculated using the maximum acceleration (a_max) and maximum velocity (v_max) as follows:

   A = v_max² / a_max

   Here, v_max is the maximum velocity, and a_max is the maximum acceleration.

2. Period (T): The period of SHM can be determined using the maximum velocity (v_max) and the amplitude (A) as follows:

   T = 2πA / v_max

   Here, v_max is the maximum velocity, and A is the amplitude.

By applying these formulas, you can calculate the amplitude and period of SHM when the maximum acceleration and maximum velocity are known.