Physics - Oscillations
Exam Duration: 45 Mins Total Questions : 30
In the case of simple pendulum, executing simple harmonic motion, the force supplying centripetal acceleration is
- (a)
\(mgcos\theta \)
- (b)
\(mgsin\theta \)
- (c)
\(-mgcos\theta \)
- (d)
\(-mgsin\theta \)
If the spring-mass system is a very high altitude, the natural frequency of longitudinal vibration
- (a)
decreases
- (b)
increases
- (c)
becomes infinite
- (d)
remains unchanged
A mass M is attached to a spring whose upper end is fixed. The mass and stiffness k of the spring are m and k respectively. The natural frequency of the spring-mass system is
- (a)
\(\nu =\frac { 1 }{ 2\pi } \sqrt { \frac { k }{ M+m } } \)
- (b)
\(r=\frac { 1 }{ 2\pi } \sqrt { \frac { k }{ M } } \)
- (c)
\(\nu =\frac { 1 }{ 2\pi } \sqrt { \frac { 3k }{ 3M+m } } \)
- (d)
\(r=\frac { 1 }{ 2\pi } \sqrt { \frac { 3k }{ M+3m } } \)
For a simple pendulum in motion, if the effect of air resistance is taken into account, which parameter is constant of motion
- (a)
Energy
- (b)
Angluar momentum
- (c)
Restoring force
- (d)
Frequency of vibration
In a spring-mass system, of mass m and stiffness k, the ends of the spring are securely fixed and mass is attached to intermediate point of spring. The natural frequency of longitudinal vibration of the system.
- (a)
is minimum when the mass is attached to the mid-point of the spring
- (b)
is maximum when the mass is attached to the mid-point of the spring
- (c)
decreases as the distance from the bottom end whose mass is attached,decreases
- (d)
decreases as the distance from the top and where mass is attached, decreases
A light spring AC of stiffness 2k is cut at B into two halves AB and BC. The point A is connected to a upper rigid support whereas point C is connected to a lower rigid support. The common point B is connected to a certain mass m. The new system will vibrate with frequency, as compared to spring AC with the same mass m,
- (a)
\(\sqrt { 2 } \) times the previous value
- (b)
2 times the previous value
- (c)
4 times the previous value
- (d)
2\(\sqrt { 2 } \) times the previous value
During the oscillations of a simple pendulum, the tension in the spring
- (a)
is greatest at its extreme position
- (b)
is zero at ats extreme position
- (c)
is greatest at its mean position
- (d)
is independent of mass
- (e)
is least at its mean position
Two simple pendulums of lengths 20 cm and 80 cm are slightly displaced in the same direction and at the same instant. Both pendulums will again be in phase after the shorter pendulum has completed
- (a)
4 oscillations
- (b)
2 oscillations
- (c)
1 oscillations
- (d)
1/2 oscillations
Consider the statements:
A. A body can have zero velocity and still be accelerating.
B. A body can have a northward velocity while experiencing a southward acceleration.
C. A body can have a constant speed and still have a varying velocity.
- (a)
A is correct only
- (b)
B is correct only
- (c)
C is correct only
- (d)
A,B,C are correct
A seconds pendulum is placed in an elevator at rest. When the elevator ascends with an acceleration \(4.9m{ s }^{ 2 }\),the pendulum will have time period (in s)
- (a)
2
- (b)
\(2\sqrt { 2 } \)
- (c)
\(2\sqrt { 3 } \)
- (d)
\(\sqrt { \frac { 8 }{ 3 } } \)
Simple harmonic motion is characterised as acceleration of a body is proportional to
- (a)
rate of change of velocity
- (b)
velocity
- (c)
mass
- (d)
NONE OF THE ABOVE
A helical spring of negligible mass is found to extend 0.25 mm under a mass of 1.5 kg. If mass 1.5 kg is replaced by mass of 60 kg, the system now will vibrate with a frequency of
- (a)
4.98 vibrations per second
- (b)
31.32 vibrations per second
- (c)
10.5 vibrations per second
- (d)
NONE OF THE ABOVE
A particle moving along a straight line vibrates to and fro about the origin of a cartesian system. While passing through the origin it has
- (a)
zero potential energy and maximum kinetic energy
- (b)
minimum potential energy and maximum kinetic energy
- (c)
maximum potential energy and minimum kinetic energy
- (d)
minimum potential energy and minimum kinetic energy
In problem Q.No. 32, the speed of the block when it reaches. \({ x }_{ 1 }=5cm\) position, after it is released from position \({ x }_{ 2 }=25cm\), is
- (a)
\(2.284{ ms }^{ -1 }\)
- (b)
\(1.142{ ms }^{ -1 }\)
- (c)
\(0.571{ ms }^{ -1 }\)
- (d)
\(4.568{ ms }^{ -1 }\)
A spring stretches by 3.0 cm from its released length when a force of 7.5 N is applied. A particle with a mass of 0.50 kg is attached to the free end of the spring, which is then compressed horizontally by 5.0 cm from its released length and released from rest at t=0. Then equation of motion of mass is
- (a)
\(x(t)=5.0sin\left( 22.36t+\frac { \pi }{ 2 } \right) \)
- (b)
\(x(t)=0.05sin\left( 22.36t+\frac { 3\pi }{ 2 } \right) \)
- (c)
\(x(t)=5.0sin\left( 22.36t+\frac { 3\pi }{ 2 } \right) \)
- (d)
\(x(t)=0.05sin\left( 22.36t+\frac { \pi }{ 2 } \right) \)
A slender uniform rod with a length l is suspended from one end. It executes oscillatory motion. The period of the rod is
- (a)
greater than that of a simple pendulum of the same length by a factor of \(\sqrt { 3 } \)
- (b)
less than that of a simple pendulum of the same length by a factor of \(\sqrt { 3 } \)
- (c)
is the same as that of a simple pendulum of the same length
- (d)
Insufficient data to calculate the period of the rod
A particle that hangs from an ideal spring has an angular frequency for oscillations, \({ \omega }_{ 0 }=2\quad rad{ \quad s }^{ -1 }\). The spring is suspended from the ceiling of an elevator car and hangs motionless (relative to the elevator car) as the car descends at a constant velocity of \(1.5{ ms }^{ -1 }\). The car then stops suddenly. The equation of motion for the particle is
- (a)
\(x=0.35sin(2t+3\pi )\)
- (b)
\(x=0.075sin(2t+\pi )\)
- (c)
\(x=0.25sin(2t+\frac { \pi }{ 2 } )\)
- (d)
\(x=0.75sin(2t+\pi )\)
A block rests in a flat plate that executes vertical SHM with a period of 1.2s. The maximum amplitude of the motion for which the block will not separate from the plate is
- (a)
35.7 cm
- (b)
0.357 cm
- (c)
18.0 cm
- (d)
12.8 cm
A block with a mass M = 0.50 kg is suspended at rest from a spring with spring constant k=200 Nm−1. A blob of putty (m=0.30 kg) is dropped onto the block from a height of 10 cm; the putty slicks to the block. The total energy of the oscillating system is
- (a)
0.132 J
- (b)
1.32 J
- (c)
0.120 J
- (d)
13.2 J
A particle that is attached to a vertical spring is pulled down a distance of 4.0 cm below its equilibrium position and is released from rest. The initial upward acceleration of the particle is 0.30 \({ ms }^{ -2 }\). The period T of the ensuring oscillations is
- (a)
1.20 s
- (b)
1.09 s
- (c)
2.29 s
- (d)
3.39 s
The displacement y of particle executing periodic motion is given by \(y=4{ cos }^{ 2 }(t/2)sin(1000t)\) this expression may be considered to be a result of the superposition of how many independent harmonic motions
- (a)
Five
- (b)
Two
- (c)
Three
- (d)
Four
The length of a simple pendulum is increased by 1%. Its time period will
- (a)
increase by 2%
- (b)
increase by 1%
- (c)
increase by 0.5%
- (d)
decrease by 0.5%
A linear oscillator of force constant \(2\times { 10 }^{ 6 }N{ m }^{ -1 }\)and amplitude 0.01 m has a total mechanical energy of 160 J.
A. Its minimum P.E.is zero
B. Its minimum P.E.is 160 J
C. Its maximum K.E.is 100 J
D. Its maximum P.E. is 100 J
- (a)
if A and B are correct
- (b)
if B and C are correct
- (c)
if C and D are correct
- (d)
if D is correct only
A particle executes simple harmonic motion with a frequency f. The frequency with which its kinetic energy oscillates is
- (a)
f
- (b)
2f
- (c)
4f
- (d)
f/2
The length of cm elastic string is x metres when the tension is 4 N and 'y' metres when tension is 5 N. The length is metres when the tension is 9 N is
- (a)
x+y
- (b)
\(2y-\frac { x }{ 4 } \)
- (c)
5y-4x
- (d)
9y-9x
The potential energy of a particle moving in SHM is 1/2 kx2. If the frequency of the particle is f, the frequency of oscillation of potential energy is
- (a)
f
- (b)
2f
- (c)
f/2
- (d)
\(\sqrt { 2 } f\)
The angular velocity, and the amplitude of a simple pendulum is \('\omega '\)and 'a'. At a displacement x from the mean position, the kinetic energy is T and the potential energy is V. Then the ratio of T to V is
- (a)
\(\frac { { x }^{ 2 }{ \omega }^{ 2 } }{ { A }^{ 2 }-{ x }^{ 2 }{ \omega }^{ 2 } } \)
- (b)
\(\frac { { x }^{ 2 } }{ { A }^{ 2 }-{ x }^{ 2 } } \)
- (c)
\(\frac { { { A }^{ 2 }-x }^{ 2 }{ \omega }^{ 2 } }{ { x }^{ 2 }-{ x }^{ 2 }{ \omega }^{ 2 } } \)
- (d)
\(\frac { { A }^{ 2 }-{ x }^{ 2 } }{ { x }^{ 2 } } \)
A particle executes simple harmonic motion between x=-A and x= +A. The time taken for it to go from 0 to A/2 is T1 and to go from A/2 to A is T2. Then
- (a)
T1
2 - (b)
T1>T2
- (c)
T1=T2
- (d)
T1=2T2