Question

a simple harmonic motion is described by a = - 16 X where a = acceleration in m/s² and X = displacement in metre calculate the time period in it

Answer 1

From the question,  

Acceleration a = -16X

X = Displacement.

In Simple Harmonic Motion, the acceleration is defined as

a = -ω^2(X)

ω = Angular Velocity.

X = Displacement

Comparing the above 2 equations, we get  

ω^2 = 16 Thus we get ω = 4.

Time period in Simple Harmonic Motion is defined as

T = 2π/ ω

T = 2*22/(7*4) = 1.57 Seconds.