Physics - Oscillations
Exam Duration: 45 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
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
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
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
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 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 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 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
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 particle moves such that its acceleration 'a' is given by a=-bx, x is displacement from equilibrium position and b is a constant. The period of oscillation is
- (a)
\(\frac { 2\pi }{ \sqrt { b } } \)
- (b)
\(2\sqrt { \frac { \pi }{ b } } \)
- (c)
\(2\pi \sqrt { b } \)
- (d)
\(\frac { 2\pi }{ b } \)
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
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
A particle of mass m is executing S.H.M. about the origin along x-axis. The P.E. U(x) = kx3 where k is positive constant. If the amplitude of oscillation is a, then time period T is proportional to
- (a)
\(\frac { 1 }{ \sqrt { a } } \)
- (b)
\(\sqrt { a } \)
- (c)
\({ a }^{ 3/2 }\)
- (d)
independent of a
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 test tube of cross-section 'a' has some lead shots at the bottom so that total mass of the tube is 'm'. It floats vertically in a liquid of density d. It is then pushed through a distance into the liquid and released If l is length of the tube dipping initially, in the liquid, the time period of oscillation is
- (a)
\(T=2\pi \sqrt { \frac { l }{ g } } \)
- (b)
\(T=2\pi \sqrt { \frac { m }{ g } } \)
- (c)
\(T=2\pi \sqrt { \frac { md }{ g } } \)
- (d)
\(T=2\pi \sqrt { \frac { md }{ ag } } \)
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
When the displacement is half of the amplitude, then what fraction of the total energy of a simple harmonic oscillator is kinetic?
- (a)
2/7th
- (b)
3/4th
- (c)
2/9th
- (d)
5/7th
A particle starts S.H.M. from the mean position. Its amplitude is A and time period is T. At the time when its speed is half of the maximum speed, its displacement y is
- (a)
\(\frac { A }{ 2 } \)
- (b)
\(\frac { A }{ \sqrt { 2 } } \)
- (c)
\(\frac { A\sqrt { 3 } }{ 2 } \)
- (d)
\(\frac { 2A }{ \sqrt { 3 } } \)