Simple Harmonic Motion MSQ - IIT JAM MCQ

The force which describe a simple harmonic motion is a second order linear differential equation 

Second-order linear differential equations have a variety of applications in science and engineering.

The correct answers are: Force is a negative gradient of the potential, The points at which the gradient of potential are the points of stable equilibrium, The points with a negative gradient of the potential are the points of unstable equilibrium

The period for a simple pendulum does not depend on the mass or the initial anglular displacement, but depends only on the length L of the string and the value of the gravitational field strength g.

So the correct answers are: The time period of two simple pendulum with different masses can be same, The time period of the simple pendulum depends only on length and gravitational acceleration.

The correct answers are: restoring force must be proportional to displacement with negative sign, existence of point of stable equilibrium, presence of inertia

The correct answer is: Is a constant because the kinetic energy & potential energy at any point add upto a constant value.

Potential energy (U) = (½)kx²

Kinetic energy (K) = (½)kA² – (½)kx²

Given, U = K

(½)kx² = (½)kA² – (½)kx² 

Lissajous figures are the path traced by a particle when acted upon by two mutually perpendicular simple harmonic motions (SHMs) simultaneously.

Lissajous figures are named after the French physicist Jules Antoine Lissajous, who studied the patterns formed by the intersection of two simple harmonic motions. When a particle is acted upon by two mutually perpendicular SHMs simultaneously, it traces a path that can take the form of a variety of different shapes, such as circles, ellipses, and figure-eight shapes. The specific shape of the Lissajous figure depends on the relative phases and amplitudes of the two SHMs, as well as the frequency ratio between them.

Option 1, "The figure depends is an ellipse in general when the two frequencies are same," is incorrect. The shape of a Lissajous figure can take the form of many different shapes, not just an ellipse.

Option 2, "Lissajous figure is the path traced by a particle when acted upon by any two SHM’s simultaneously," is correct.

Option 3, "Lissajous figure is the path traced by a particle when acted upon by two mutually perpendicular SHMs simultaneously," is correct.

Option 4, "The figure is a straight line in general," is incorrect. Lissajous figures are typically curved, not straight.

The correct answers are: varies with time, maximum at x = 0 and minimum at the extreme positions of the oscillations.

Periodic time is the time taken for one complete revolution of the particle.

∴ Periodic time, tp = 2 π/ω seconds.

When a rigid body is suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as compound pendulum. Thus the periodic time of a compound pendulum is minimum when the distance between the point of suspension and the centre of gravity is equal to the radius of gyration of the body about its centre of gravity.