Question

The displacement time graph of a particle executing S.H.M. (in straight line) is shown. Which of the following statements is incorrect ?

• A. the velocity is maximum at t $=\frac{T}{2}$
• B. the acceleration is maximum at t $=T$
• C. the force is zero at t $=\frac{3T}{4}$
• D. the potential energy equals the total oscillation energy at t $=\frac{T}{2}$

Answer 1

Answer: (D)

the potential energy equals the total oscillation energy at t $=\frac{T}{2}$

We know that velocity is maximum when the particle is at its mean position i.e.at $t=\frac{T}{4},\frac{3T}{4}$. Thus A is incorrect.
The acceleration ,$\frac{d^{2}y}{d{t}^2}$ is maximum at the extreme position i.e. at $t=0,\frac{T}{2}andT$. Thus, B is correct.
Force is zero where acceleration is zero i.e. at $t=\frac{T}{4}and\frac{3T}{4}$ Thus C is correct.
As the interval of max and min displacement is $\frac{T}{2}$, so the potential energy equals the oscillation at $\frac{T}{2}$. Thus D is correct.