Engineering Questions with Answers - Multiple Choice Questions
Oscillations – 2
A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The speed of the pendulum at x = a/2 will be ___________
d) (3π2 a)/T
A body is executing simple harmonic motion. When the displacements from the mean position are 4cm and 5cm, the corresponding velocities of the body are 10cm/sec and 8cm/sec. Thenwhat is the time period of the body?
a) 2π sec
b) π/2 sec
c) π sec
d) 3π/2 sec
The total energy of a particle performing simple harmonic motion depends on ___________
a) k, a, m
b) k, a
c) k, a, x
d) k, x
Explanation: E=1/2×mω2 a2=1/2×ka2
Clearly, E depends on k and a.
The particle executing simple harmonic motion has a kinetic energy K0 cos2 ωt. The maximum values of the potential energy and the total energy are respectively ___________
a) Kc/2 and K0
b) K0 and K0
c) K0 and 2K0
d) 0 and 2K0
Explanation: When kinetic energy is maximum, potential energy is zero and vice-versa. But
Kinetic energy+ Potential energy = Total energy
Maximum potential energy = Maximum kinetic energy = Total energy = K0.
A linear harmonic oscillator of force constant 2×106 N/m and amplitude 0.01m has a total mechanical energy of 160J. Its ___________
a) Potential energy is 160 J
b) Potential energy is zero
c) Potential energy is 100J
d) Potential energy is 120J
Explanation: Potential energy = 1/2×kx2
The potential energy of a simple harmonic oscillation when the article is halfway to its end point is ___________
a) 2/3 E
b) 1/8 E
c) 1/4 E
d) 1/2 E
In a simple harmonic motion, when the displacement is one half the amplitude, what fraction of the total energy is kinetic?
Explanation: At x = a/2, the kinetic energy is
Kinetic energy=1/2×k×[a2-(a/2)2]=3/4×1/2×ka2=3/4 E.
A body executes simple harmonic motion with amplitude A. At what displacement from the mean position is the potential energy of the body one fourth of its total energy?
d) Some other fraction of A
Explanation: Potential energy = 1/4×Total energy
A loaded vertical spring executes simple harmonic motion with a time period of 4 sec. The difference between the kinetic energy and potential energy of this system varies with a period of?
a) 2 sec
b) 1 sec
c) 8 sec
d) 4 sec
Explanation: Here T=4s. In one oscillation, both kinetic energy and potential energy become twice maximum and twice minimum. Hence the difference between kinetic energy and potential 2s.
A mass m is vertically suspended from a spring of negligible mass; the system oscillates with a frequency n. What will be the frequency of the system, if a mass 4m is suspended from the same spring?