Question

The graph shows variation of displacement of a particle performing SHM with time t. which of the following statements is correct from the graph?

• A. The acceleration is maximum at time \(T\).
• B. The force is maximum at time \(\frac{3T}{4}\).
• C. The velocity is zero at time \(\frac{T}{2}\).
• D. The kinetic energy is equal to total energy at time \(\frac{T}{4}\).

Hint:

Match each time with the particle position on the graph: the force is largest where the displacement is largest.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In SHM, acceleration and restoring force are proportional to displacement, \(F=-kx\). Speed and kinetic energy are maximum at the mean position and zero at the extremes.

Step 2: Calculation
From the graph the particle is at the mean position at \(\frac{T}{2}\) and \(T\), and at an extreme position at \(\frac{T}{4}\) and \(\frac{3T}{4}\).

Step 3: Compare the options
At \(T\) the acceleration is zero, so option A fails. At \(\frac{T}{2}\) the speed is maximum, so option C fails. At \(\frac{T}{4}\) the particle is at an extreme where the kinetic energy is zero, so option D fails. At \(\frac{3T}{4}\) the displacement is largest, so the force is maximum (option B).

Final Answer:
The force is maximum at time \(\frac{3T}{4}\). \[ \boxed{\text{(B) }\text{The force is maximum at time }\dfrac{3T}{4}} \]