Oscillations Test

Result

Oscillations Test - 72

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Question 1
1 / -0

Two particles are in SHM in a straight line about same equilibrium position. Amplitude $$A$$ and time period $$T$$ of both the particles are equal. At time $$t = 0$$, one particle is at displacement $$y_{1} = +A$$ and the other at $$y_{2} = -A/2$$, and they are approaching towards towards each other. After what time they cross each other?

A
$$T/3$$

B
$$T/4$$

C
$$5T/6$$

D
$$T/6$$
Question 2
1 / -0

A particle makes SHM along a straight and tis velocity when passing through point $$3cm$$ and $$4cm$$ from the mean position $$16mc/sec$$ and $$12cm/sec$$ respectively. then time period is

A
$$\dfrac{\pi}{2}sec$$

B
$$\pi sec$$

C
$$\dfrac{3\pi}{2}sec$$

D
$$2\pi sec$$

Solution
Question 3
1 / -0

A thin hoop of radius r and mass m is suspended from a rough rod as shown. Determine the time period of small oscillaion of the hoop in a direction perpendicular to the plane of the hoop. Assume that friction is sufficiently large to prevent slipping at A.

A
$$2 \pi \sqrt {\cfrac g R}$$

B
$$2 \pi \sqrt {\cfrac {3R} {2g}}$$

C
$$2 \pi \sqrt {\cfrac R {2g}}$$

D
None

Solution
Question 4
1 / -0

A particle is executing SHM with time period T.Starting from mean position, time taken by it to complete $$cfrac 5 8$$ oscillations, is

A
$$\cfrac T {12}$$

B
$$\cfrac T {6}$$

C
$$\cfrac {5T} {12}$$

D
$$\cfrac {7T} {12}$$

Solution
Question 5
1 / -0

A loaded vertical spring executes S.H.M with a time period of $$4$$ s. The difference in time between the max. K.E. and max. P.E. of this system varies with a period of

A
$$1$$ s

B
$$2$$ s

C
$$4$$ s

D
$$8$$ s

Solution
Question 6
1 / -0

The motion represented by equation $$x=2\sin \omega t+3\sin^{2}\omega t$$ is

A
Periodic

B
Oscillatory

C
$$SHM$$

D
Both (1) & (2)
Question 7
1 / -0

A particle executes simple harmonic motion and is located at $$x = a, b$$ and $$c$$ at times $$t_{0}, 2t_{0}$$ and $$3t_{0}$$ respectively. The frequency of the oscillation is

A
$$\dfrac {1}{2\pi t_{0}}\cos^{-1} \left (\dfrac {a + c}{2b}\right )$$

B
$$\dfrac {1}{2\pi t_{0}}\cos^{-1} \left (\dfrac {a + b}{2c}\right )$$

C
$$\dfrac {1}{2\pi t_{0}}\cos^{-1} \left (\dfrac {2a + 3c}{2b}\right )$$

D
$$\dfrac {1}{2\pi t_{0}}\cos^{-1} \left (\dfrac {a + 2b}{3c}\right )$$
Question 8
1 / -0

A $$1.8$$ g mass suspended by a spring with a spring constant of $$3$$ N/m is forced to oscillate in viscous medium (b=$$2$$ g/s) by a driving force of F=$${10^{ - 3}}$$ sin$$40$$t (in SI units). the amplitude of the driven oscillations will be

A
$$3.4 \times {10^{ - 6}}{m^2}$$

B
$$3.6 \times {10^{ 5}}{m^2}$$

C
$$3.4 \times {10^{ 3}}{m^2}$$

D
$$2.4 \times {10^{ 2}}{m^2}$$
Question 9
1 / -0

Initially mass m is held such that spring is in relaxed condition . if mass m is suddenly released maximum elongation in spring will be

A
$$ \dfrac {mg}{k} $$

B
$$ \dfrac {2mg}{k} $$

C
$$ \dfrac {mg}{2k} $$

D
$$ \dfrac {mg}{4k} $$

Solution
Question 10
1 / -0

A pendulum bob of weight IN is beld at an angle $$\theta$$ from the vertical by a horizontal force of 2$$N$$ ashown. The tension in the string supporting the pendulum bob (in newton) is

A
$$\frac { 1 } { \cos \theta }$$

B
$$\frac { 2 } { 2 \sin \theta }$$

C
$$\sqrt { 15 }$$

D
1

Solution