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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
Secondorder 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
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
Let x=Asinωt
Then, v=dx/dt=Aωcos(ωt)
K.E.= 1/2mv^{2}
Average kinetic energy is 1/T∫(T to 0)1/2mv^{2}dt=1/4mA^{2}ω^{2}
Average potential energy is
1/T∫(T to 0) 1/2kx^{2}dt= 1/4mA^{2}ω^{2}
The correct answer is option D.
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.
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
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.
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