A body executes SHM with aperiod of 11/7 s and an amplitude of 0.025 m. What is the maximum value of acceleration?

What is the force equation of a SHM?

If the length of a simple pendulum is increased by 25% then what is the change in its time period?

State the condition when motion of a particle can be an SHM.

A simple harmonic motion given by \(x=6.0\quad cos\left( 100t+\frac { \pi }{ 4 } \right) \) where x is in cm and t in second. What is the (i) displacement amplitude, (ii) frequency?

Which of the following examples represent periodic motion?
(i) A freely suspended bar magnet displaced from its N-S direction and released.
(ii) A hydrogen molecule rotating about its centre of mass.
(iii) An arrow released from a bow.

Every SHM is periodic motion, but every periodic motion need not to be a simple harmonic motion. Do you agree? Give an example to justify your statement.

What is the total energy of a simple harmonic oscillator?

The length of a second pendulum on the surface of earth is 1m. What will be the length of a second pendulum on the moon?

A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period ?

A block with a mass of 3.0 kg is suspended from an ideal spring having negligible mass and stretches the spring by 0.2 m.
(a) What is the force constant of the spring?
(b) What is the period of oscillation of the block if it is pulled down and released?

A horizontal platform with an object placed on it is executing SHM in the vertical direction. The amplitude of oscillation is 2.5 cm. What must be the least period of these oscillations so that the object is not detached from the platform? Take g = 10 ms^-2?

Samar invited his friends for a party at his house. His friends were enjoying the party and jumping on the sofa. They started the competition of high jump on the sofa.Samar's father warned them that the springs of sofa could be broken and they could get hurt and explained them the working of spring. Children promised that they would never jump on the furniture.
(i) What values of the boys do you appreciate?
(ii) A spring compressed by 0.2 m develops a restoring force of 20 N. A body of mass 4 kg is placed on it. Deduce (a) the force constant of spring (b) depression of the spring under the weight of the body.
(iii) Give two examples of objects which work using springs.

A simple harmonic motion is represented by \(x=12\sin { \left( 10t+0.6 \right) } \) Find out the amplitude, angular frequency, frequency, time period and initial phase if displacement is measured in metre and time in seconds.

Two linear simple harmonic motions of equal amplitudes and frequencies ω and 2ω are impressed on a particle along the axes of X and Y respective/yo If the initial phase difference between them is π/2 find the resultant path followed by the particle.

Figure (a) shows a spring of force constant k clamped rigidly at one-end and a mass m attached to its free end. A force F applied at the free end stretches the spring. Figure (b) shows the same spring with both ends free and attached to a mass m at either end. Each end of the spring in Figure (b) is stretched by the same force F.

(a) What is the maximum extension of the spring in the two cases?
(b) If the mass in Fig. (a) and the two masses in Fig. (b) are released free, what is the period of oscillation in each case?

A uniform spring whose unstretched length is I has a force constant k. The spring is cut into two pieces of unstretched lengths. l₁and l₂, where l₁= nl₂ and n is an integer. What are the corresponding force constants k₁ and k₂ in terms of n and k?