Oscillations quiz

In SHM, the acceleration is proportional to:

At the mean position in SHM, the speed is:

The period of a simple pendulum for small oscillations:

The period of a seconds pendulum is:

The total energy of a particle in SHM is proportional to:

The period of a mass-spring system:

In SHM, kinetic energy equals potential energy when the displacement is:

The phase difference between displacement and velocity in SHM is:

Frequency is related to period by:

If a spring is cut into two equal halves, the spring constant of each half is:

Is the motion of the Earth around the Sun periodic? Is it oscillatory? Explain. (2 marks)

Which of these is periodic: sin(omega t) + cos(omega t) or e^(-omega t)? Give the period if periodic. (2 marks)

Write the force law for simple harmonic motion. (2 marks)

Show that in SHM, v = omega sqrt(A^2 - x^2). (2 marks)

What happens to the period of a pendulum taken to the Moon? (2 marks)

How does the period of a pendulum change in a lift accelerating upwards? (2 marks)

Define phase and phase constant. (2 marks)

Why is the restoring force in a simple pendulum approximately proportional to displacement only for small angles? (2 marks)

A particle in SHM has period 2 s. Find its angular frequency. (2 marks)

What is the period of a spring oscillator if the spring is cut in half and the same mass is used? (2 marks)

A 0.5 kg mass on a spring of k = 50 N/m oscillates with amplitude 4 cm. Find the period and the maximum speed. (3 marks)

Find the length of a pendulum with a period of 4 s. Take g = 9.8 m/s^2 and pi^2 = 9.8. (3 marks)

A particle in SHM has amplitude 10 cm and period 0.2 s. Find its acceleration when the displacement is 5 cm. (3 marks)

A body in SHM has a maximum speed of 1 m/s and a maximum acceleration of 10 m/s^2. Find its amplitude and angular frequency. (3 marks)

A pendulum clock beats seconds correctly at a place where g = 9.8 m/s^2. Find its period at a place where g = 9.6 m/s^2. (3 marks)

Read the passage and answer the questions. A child sits on a swing of length 2.5 m and swings with small amplitude. Take g = 9.8 m/s^2. (i) Find the period of the swing. (ii) Does the period change if a heavier child sits on it? (iii) Does the period change if the child stands up? Explain. (5 marks)

Read the passage and answer the questions. A spring balance stretches 5 cm when a mass of 0.5 kg hangs from it. The mass is then pulled down a little and released. (i) Find the spring constant. (ii) Find the period of oscillation. (iii) How does the period change if the mass is doubled? (5 marks)

Read the passage and answer the questions. A pendulum clock is accurate at sea level. It is taken to the top of a high mountain. (i) What happens to g there? (ii) Does the clock gain or lose time? (iii) How can the clock be corrected? (5 marks)

Read the passage and answer the questions. A particle moves in SHM with x = 0.1 cos(4t) metres. (i) Find the amplitude and the period. (ii) Find the maximum speed. (iii) Find the maximum acceleration. (5 marks)

Read the passage and answer the questions. A block of mass 2 kg on a spring of k = 200 N/m oscillates with amplitude 0.05 m. (i) Find the total energy. (ii) Find the maximum speed. (iii) Find the potential energy at the mean position. (5 marks)

Explain periodic and oscillatory motion. Define period, frequency, amplitude, phase and angular frequency with examples. (6 marks)

Show that SHM is the projection of uniform circular motion on a diameter. Derive expressions for velocity and acceleration in SHM. (6 marks)

Derive the expressions for the kinetic, potential and total energy of a particle in SHM, and show the variation graphically. (6 marks)

Derive the period of a simple pendulum and state the factors on which it depends and does not depend. (6 marks)

Explain the force law for SHM and show that a mass attached to a vertical spring also performs SHM. (6 marks)