The force which does not describe a simple harmonic motion is
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.
Choose the correct statements for the case of a one dimensional simple harmonic motion.
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
When the phase difference between two mutually perpendicular SHMs is a quarter integer multiple of π then the path traced by a particle on which they act can be
The correct answers are: an oblique ellipse a with the major axis making an obtuse angle with x-axis, a straight line
Select the correct options
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
The physical condition for simple harmonic motion is/are
The correct answers are: restoring force must be proportional to displacement with negative sign, existence of point of stable equilibrium, presence of inertia
For a particular case of simple harmonic motion the total energy
The correct answer is: Is a constant because the kinetic energy & potential energy at any point add upto a constant value.
Select the correct options for a particle undergoing simple harmonic motion
Average kinetic energy is 1/T∫(T to 0)1/2mv2dt=1/4mA2ω2
Average potential energy is
1/T∫(T to 0) 1/2kx2dt= 1/4mA2ω2
Choose the correct option for Lissajous figures :
The correct answers are: Lissajous figure is the path traced by a particle when acted upon by two mutually perpendicular SHMs simultaneously, The figure depends is an ellipse in general when the two frequencies are same
Velocity of a particle undergoing simple harmonic motion is
The correct answers are: varies with time, maximum at x = 0 and minimum at the extreme positions of the oscillations.
When a particle is being acted upon by two mutually perpendicular SHMs with same frequency & same amplitude then it traces a path which is