For a body moving with simple harmonic motion state the equations to represent: i) velocity ii) acceleration iii) periodic time iv) frequency v) on a diagram show the positions of max and min values for acceleration and velocity and show using the equations why this is the case.

Answer with Explanation:

The general equation of simple harmonic motion is

where,

A is the amplitude of motion

is the angular frequency of the motion

is known as initial phase

part 1)

Now by definition of velocity we have

part 2)

Now by definition of acceleration we have

part 3)

The angular frequency is related to Time period 'T' as

where

is the angular frequency of the motion of the particle.

Part 4) The acceleration and velocities are plotted below

since the maximum value that the sin(x) and cos(x) can achieve in their respective domains equals 1 thus the maximum value of acceleration and velocity is and respectively.