In case of simple harmonic motion, displacement is proportional to the

ANS:B - acceleration

In simple harmonic motion (SHM), displacement is proportional to the acceleration, not the velocity. The equation of motion for simple harmonic motion is typically given by: x=A⋅sin(ωt+ϕ) Where:

• x is the displacement from the equilibrium position,
• A is the amplitude of the motion,
• ω is the angular frequency,
• t is time, and
• ϕ is the phase angle.

Taking the second derivative of the displacement equation with respect to time (d^2x/dt^2​), we find that acceleration (a) is proportional to displacement (x) and has the opposite direction: a=−ω^2x Therefore, in simple harmonic motion, displacement (x) is directly proportional to the acceleration (a), but it is not directly proportional to velocity (v). However, velocity and acceleration are related through the derivative of displacement with respect to time: v=dt/dx​ So, velocity is proportional to the rate of change of displacement with time, and acceleration is proportional to the rate of change of velocity with time. Therefore, both displacement and velocity are related to acceleration in simple harmonic motion, making the correct choice (b) both (a) & (b).