JEE Main Physics - Oscillations
Exam Duration: 60 Mins Total Questions : 30
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
The following equation represents the displacement y (in m) of a particle executing simple harmonic motion as a function of time t
\(y=0.6sin(4\pi t+0.5\pi )cos(4\pi t+0.5\pi )\) It has frequency,initial phase and amplitude respectively as
- (a)
4 Hz,0.5 rad and 0.6 m
- (b)
4 Hz,\(\pi \) rad and 0.3 m
- (c)
8 Hz, 0.5 rad and 0.3 m
- (d)
8 Hz,\(\pi \) rad and 0.6 m
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 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)
\(\sqrt { \frac { 8 }{ 3 } } \)
Two masses M and 16M are suspended from two identical springs. They are given small displecements in the same direction and at the same instant. They will be out of phase after mass M has completed
- (a)
one oscillation
- (b)
2 oscillations
- (c)
4 oscillations
- (d)
8 oscillations
A body is placed on a horizontal plateform which executes simple harmonic motion with a period of 4s. When the amplitude of plateform just exceeds 20 cm, the body starts sliding. The coefficient of static friction between the body and the platform is
- (a)
0.05
- (b)
0.2
- (c)
0.3
- (d)
0.6
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 mass m =2 kg is attached to a spring of stiffness \(8Nm^{ -1 }\).At time t=0 the mass is displaced to a position x=0.2 m and released from rest. The position x of the mass m is given by (in metre)
- (a)
x = 0.2 sin 2t
- (b)
\(x=0.2\quad sin\quad 4\pi t\)
- (c)
x = 0.2 cos 2t
- (d)
x = 2 cos 0.2 t
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
A spring with zero relaxed length and spring constant k = 50 \({ Nm }^{ -1 }\) moves a block by contracting from a stretched length of 25 cm to a length of 5 cm. The block of mass m = 0.5 kg slides on a horizontal frictionless surface. The amount of work done on the block by the spring is
- (a)
2.188 J
- (b)
0.50 J
- (c)
1.500 J
- (d)
15 kJ
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 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 small bob with a mass of 0.20 kg hangs at rest from a massless string with a length of 1.40 m. At t=0 the bob is given a sharp horizontal blow that delivers an impulse, \(J=\int { F\quad dt=0.15\quad Ns } \) due to which it gets an angular displacement \(\theta \). The equation of motion of the bob (in radian) is
- (a)
\(\theta (t)=0.202sin\quad 5.30t\)
- (b)
\(\theta (t)=0.404sin\quad 1.37t\)
- (c)
\(\theta (t)=0.202sin\quad 2.65t\)
- (d)
\(\theta (t)=0.303sin\quad 2.02t\)
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 \(N{ m }^{ -1 }\). 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 period of the ensuring oscillations is
- (a)
1.2 s
- (b)
0.397 s
- (c)
0.252 s
- (d)
4.2 s
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
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
Identify the correct statement among the following :
- (a)
A simple pendulum with a bob of mass M swings with an angular amplitude of 40 °. When its angular amplitude is 20 °, then the tension in the string is Mg cos 20 °.
- (b)
The greater the mass of a pendulum bob, the shorter is its frequency of oscillation.
- (c)
The fractional change in the time period of a pendulum on changing the temperature is independent of the length of the pendulum.
- (d)
As the length of a simple pendulum is increased, the maximum velocity of its bob during its oscillation will also increase.
In which case does the potential energy decrease?
- (a)
on compressing a spring
- (b)
on stretching a spring
- (c)
on moving body against gravitational force
- (d)
on the rising of an air bubble in water
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)
\(\frac { { A }^{ 2 }-{ x }^{ 2 } }{ { x }^{ 2 } } \)
For a particle executing simple harmonic motion, the kinetic energy is given by \(k={ k }_{ 0 }{ cos }^{ 2 }\omega t\). The maximum value of potential energy is
- (a)
k0
- (b)
zero
- (c)
k0/2
- (d)
not obtainable
For a particle executing simple harmonic motion, which of the following statements is correct?
- (a)
Total energy of the particle always remains the same
- (b)
Restoring force is always directed towards fixed point
- (c)
Restoring force is maximum at the equilibrium position
- (d)
Acceleration of the particle is maximum at the extreme position
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