Q1: Pick up the incorrect statement from the following. In a simple harmonic motion

ANS:C - acceleration is minimum at the end of the stroke

Acceleration is a measure of the rate of change of velocity with respect to time. In the context of simple harmonic motion (SHM), which describes the motion of an object back and forth around an equilibrium point, acceleration varies throughout the motion. Let's consider the motion of an object undergoing SHM, such as a mass attached to a spring. As the mass oscillates back and forth, its velocity and acceleration change continuously. At the end of the stroke, when the object reaches its maximum displacement from the equilibrium position, the velocity momentarily becomes zero. This occurs because at the extreme positions, the object momentarily stops before reversing its direction. However, the acceleration, which is the rate of change of velocity, is at its maximum magnitude at these extreme positions. This is because as the object reverses its direction, the velocity changes rapidly, and acceleration is at its maximum to effect this change in velocity. Conversely, at the mean position (the equilibrium point), the velocity is at its maximum magnitude, as the object is moving at its highest speed during its oscillation. At this point, the object has the maximum kinetic energy in its oscillatory motion. At the mean position, where the velocity is maximum, the acceleration is zero. This is because the object is momentarily stationary at this point, so there is no change in velocity, and hence no acceleration. In summary:

• Velocity is minimum (zero) at the end of the stroke.
• Acceleration is maximum at the end of the stroke, where the velocity changes rapidly.
• Velocity is maximum at the mean position.
• Acceleration is zero at the mean position, where the velocity is constant.