For a particle executing simple harmonic motion, the displacement x is given by x=Acosωt. Identify the graph, which represents the variation of potential energy (U) as a function of time t and displacement x.

What are the conditions for a particle to execute SHM?

• There must be an elastic restoring force acting on the system.
• The system must have inertia.
• The acceleration of the system should be directly proportional to its displacement and is always directed to mean position.

When a particle executes simple harmonic motion?

A particle executes simple Harmonic Motion with amplitude of 4cm. At the mean position, the velocity of the particle is 10cm/sec. The distance of the particle from the mean position when its speed becomes 5cm/s is.

What is the kinetic energy of a particle executing SHM?

The kinetic energy of a particle executing S.H.M. is 16J when it is at its mean position if the amplitude of oscillation is 25cm , and the mass of the particle is 5.12kg then time period of the oscillation is: (A) 20πsec.

What is the time taken by a particle executing SHM?

The period time of a particle doing simple harmonic motion is 4 s.

A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The

What is the acceleration of a particle in simple harmonic motion?

The acceleration of a particle executing simple harmonic motion is given by, a(t) = -ω² x(t). Here, ω is the angular velocity of the particle.

Which function represents SHM?

sinωt+cos2ωt.

Where is the kinetic energy of a particle executing SHM minimum?

Note: Kinetic energy is zero at the extreme position as velocity is zero and potential energy is maximum. Potential energy is minimum at the mean position which is also the lowest position.

Where do the kinetic energy of particle executing SHM have maximum?

The particle will have maximum kinetic energy when it is passing through the mean position of the oscillation. At this position, the particle will only have kinetic energy and no potential energy since the particle is at the mean position.

At what point is the kinetic energy of a particle in SHM maximum?

At maximum displacement from the equilibrium point, potential energy is a maximum while kinetic energy is zero. At the equilibrium point the potential energy is zero and the kinetic energy is a maximum.

When a particle executes SHM the nature of graphical representation?

When particle executes SHM, the nature of graphical representation of velocity as a function of displacement is : Option: 1 parabolic.

What is the frequency of oscillation is a particle executing simple harmonic motion of amplitude 5cm has maximum speed of 31.4 cm sec?

A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is. 3 Hz.

On which of the following does the energy of simple harmonic motion depend?

Thus, the total energy in the simple harmonic motion of a particle is: Directly proportional to its mass. Directly proportional to the square of the frequency of oscillations and. Directly proportional to the square of the amplitude of oscillation.

What 3 conditions must be met for simple harmonic motion?

Conditions to produce simple harmonic motion include that the net force must be described by F=-kx, where F is the restoring force, x is the displace, and k is the force constant. To produce simple harmonic motion, the rate of change of velocity must be proportional to the displacement. You just studied 18 terms!

When the amplitude of a particle executing SHM is increased slightly its period?

Answer: : If amplitude of SHM is increased , time period of SHM will increase. Reason: If amplitude is increased, body have to travel more distance in one complete oscillation.

What is a SHM write down the conditions for SHM?

Condition for SHM. In order for an object to display simple harmonic motion, the resultant force acting on the object must be directly proportional to its displacement from its equilibrium point, and must act towards the equilibrium point - it must act in the opposite direction to the displacement.

Where is the potential energy of a particle executing SHM minimum and maximum?

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Potential energy of the particle executing SHM is maximum at extreme position and minimum at mean position. Time taken for particle to move from mean position to extreme position is T/4. Hence, time period of the SHM is 4×T = 4×5 = 20 s.

What is the phase difference between the displacement and velocity of a particle executing simple harmonic motion?

Therefore, for a particle executing Simple Harmonic Motion, the phase difference between velocity and displacement is equal to $\dfrac{\pi }{2}$ radian.

What is the necessary and sufficient condition for SHM?

Necessary and sufficient condition for simple harmonic motion. The restoring force must be proportional to the displacement and act opposite to the direction of motion with no drag forces or friction. The frequency of oscillation should not depend on the amplitude.

How do you determine SHM?

That is, F = −kx, where F is the force, x is the displacement, and k is a constant. This relation is called Hooke's law. A specific example of a simple harmonic oscillator is the vibration of a mass attached to a vertical spring, the other end of which is fixed in a ceiling.

Which of the following functions do not represent SHM?

Simple harmonic motion is represented by a sine function or a cosine function or a linear combination of both. Hence, options (a),(b) and (c) represent simple harmonic motion while option (d) is a product of the two functions (sine and cosine) does not represent a simple harmonic motion.

What is the differential equation of linear SHM?

The differential equation for linear SHM of a particle of mass 2g is d2xdt2+16x=0.

What is the acceleration of particle in SHM at mean position?

Since the displacement of the particle at mean position is zero, the acceleration of the particle is also zero. One should always take the displacement of the particle in SHM from the mean position where there is no restoring force acting on the particle.

What can be said about the acceleration of a particle in SHM?

If the velocity of the simple harmonic motion is maximum, the acceleration must be equal to zero. The acceleration is equal to zero only when the particle or object is at initial position or if the displacement of the particle is zero.

When a particle performs simple harmonic motion then its velocity?

When a particle perform simple harmonic motion then its B) Velocity and acceleration change continuously . So, with change in position (i.e. displacement), the velocity and acceleration continuously change.