What is the ratio of maximum acceleration to the maximum velocity of a simple harmonic oscillator?

Question

Philoid · Accepted Answer

Equation of motion for S.H.M is as follows,

Where,

x is displacement

A is the amplitude

w is the angular velocity

t is the time

for velocity, we differentiate the above equation, we get,

For max v,

----(1)

for acceleration, we differentiate the velocity equation, we get,

For max a,

----(2)

Dividing equation 2 with 1 we get,

∴ the ratio of max acceleration to max velocity is