Some Systems Executing Simple Harmonic Motion

A simple pendulum of time period 1s and length l is hung from a fixed support at O, such that the bob is at a distance H vertically above A on the ground (Figure). The amplitude is θ₀. The string snaps at θ = θ₀/2. Find the time taken by the bob to hit the ground. Also find distance from A where bob hits the ground. Assume θ_o to be small so that sin θ_o = θ_o and cos θ_o = 1.

If the metal bob of a simple pendulum is replaced by a wooden bob of the same size, then its time period will.....................

1. increase
2. remain same
3. decrease
4. first increase and then decrease.

Consider a pair of identical pendulums, which oscillate with equal amplitude independently such that when one pendulum is at its extreme position making an angle of 2° to the right with the vertical, the other pendulum makes an angle of 1° to the left of the vertical. What is the phase difference between the pendulums?

The phase difference between displacement and acceleration of a particle performing S.H.M. is _______.

(A) ${\displaystyle \frac{\pi }{2}rad}$

(B) π rad

(C) 2π rad

(D)${\displaystyle \frac{3\pi }{2}rad}$

Answer the following questions:

A time period of a particle in SHM depends on the force constant k and mass m of the particle: ${\displaystyle T=2\pi \sqrt{\frac{m}{k}}}$ A simple pendulum executes SHM approximately. Why then is the time 

A spring having with a spring constant 1200 N m^–1 is mounted on a horizontal table as shown in Fig. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.

Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.

When the length of a simple pendulum is decreased by 20 cm, the period changes by 10%. Find the original length of the pendulum.

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?