Amity School of Engineering & Technology (NOIDA)



Amity School of Engineering & Technology (NOIDA)

Applied Physics I

Tutorial Sheet: 1 (Module I: Oscillations and Waves)

1. A simple harmonic oscillator of mass 0.4 gm has amplitude of 2 cm and the velocity at zero displacement is 100 cm/s. Calculate the periodic time of oscillation and the energy of the oscillator.

2. A particle vibrates with SHM of amplitude 0.05 m and a period of 6s. How long does it take to move from one end of its path to a position 0.025 m from the equilibrium position on the same side?

3. A particle makes SHM along a straight line and its velocity when passing through points 3 cm and 4 cm from the center of its path is 16 cm /sec and 12 cm/sec respectively. Find the amplitude and time period of motion.

4. A particle is moving under SHM. When the distance of the particle from the equilibrium position has the values x[pic] and x[pic],the corresponding values of velocities are v[pic][pic] and v[pic].Show the time period is:

T=2π√x[pic]- x[pic]/ v[pic]- v[pic][pic]

5. Show that if the displacement of a moving point at any time is given by an equation of the form x=acosωt+bsinωt, the motion is simple harmonic. If a=3, b=4 and ω=2, determine its period, amplitude, maximum velocity and maximum acceleration of the motion.

6. A mass of 1.6 kg stretches a spring 0.08 m from its equilibrium position. This mass is replaces by another mass of 0.05 kg. It is pulled and released so that it starts oscillating. Find the time period of oscillation.

7. A particle of mass 0.1 kg is situated in the potential field V = 5x2+10 Joule/kg. Write down the differential equation of motion of the particle and hence determine its frequency of oscillation.

8. A particle of mass 10 g is moving along the X axis under the force 4×10-2x acting towards origin. If the initial position of the particle at t= 0 is 0.1 m, write down the differential equation of motion of particle and thus calculate frequency and amplitude of oscillation.

9. Compare the energies of two identical simple pendulums having amplitudes 2 and 6 cm respectively.

10. The amplitude of a particle of mass 100 g executing SHM is 100 cm and its kinetic energy in mean position is 8×10-3 J. Write down the equation of motion of the particle if the initial phase difference is 45o.

Tutorial Sheet: 2 (Module I: Oscillations and Waves)

1. If a particle is subjected to a restoring force proportional to displacement and a damping force proportional to velocity, calculate the displacement of the particle at any subsequent time when it is executing oscillatory motion. If the motion of the particle is critically damped, find the displacement at any instant.

2. For a damped harmonic oscillator, the relaxation time is 50s.Find the time in which the amplitude and energy of the oscillator falls to1/e times its initial value.

3. The quality factor of tuning fork is 104. Calculate the time interval, after which its energy becomes 1/10 of its initial value. The frequency of the tuning fork is 250 Hz.

4. An under damped harmonic oscillator has its amplitude reduced to 1/10th of its initial value after 100 oscillations. If its time period is 1.15s then calculate (i) damping constant (ii) relaxation time.

5. The quality factor of sonometer wire of frequency 240 Hz is 2000. Find the time in which the amplitude decreases to l/e2 of its initial value.

6. Describe how the amplitude of a weakly damped driven oscillator varies with frequency of the driving force. Discuss the cases when ( ................
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