Oscillations

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period T. If the mass is increased by m, then the time period becomes $\left(\frac{5}{4} \mathrm{T}\right)$. The ratio of $\frac{\mathrm{m}}{\mathrm{M}}$ is

• 9/16

• 5/4

• 25/16

• 4/5

A wave is represented by the equation y= 0.5 sin(10t $-$ x) metre It is a travelling wave propagating along +x direction with velocity

• 10 m s^-1

• 20 m s^-1

• 5 m s^-1

• None of these

The frequency of oscillations of a mass m connected horizontally by a spring of spring constant k is 4 Hz. When the spring is replaced by two identical spring as shown in figure. Then the effective frequency is

• 4 $\sqrt{2}$

• 1.5

• 1.31

• 2$\sqrt{2}$

Assertion:  The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola. 

Reason:  Potential energy and kinetic energy do not vary linearly with position.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Motion of an oscillating liquid in a U tube is

• periodic but not simple harmonic.

• non-periodic.

• simple harmonic and time period is independent of the density of the liquid.

• simple harmonic and time period is directly proportional to the density of the liquid.

A bottle weighing 220 g and of area of cross-section 50 cm², and height 4 cm oscillates on the surface of water in vertical position. Its frequency of oscillation is

• 1.5 Hz

• 2.5 Hz

• 3.5 Hz

• 4.5 Hz

The time period of a particle undergoing SHM is 16 s. It starts motion from the mean position. After 2 s, its velocity is 0.4 m s^-1 .The amplitude is

• 1.44 m

• 0.72 m

• 2.88 m

• 0.36 m

A 5.5 metre length of string has a mass of 0.035 kg. If the tension in the string is 77 N, the velocity of the wave on the string is

• 210 m s^-1

• 40 m s^-1

• 110 m s^-1

• 55 m s^-1

Assertion:  The periodic time of a hard spring is less as compared to that of a soft spring. 

Reason:  The periodic time depends upon the spring constant, which is large for hard spring.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

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

• $\frac{\mathrm{\pi } \mathrm{\alpha }}{\mathrm{T}}$

• $\frac{3 {\mathrm{\pi }}^2 \mathrm{a}}{\mathrm{T}}$

• $\frac{\mathrm{\pi } \mathrm{a}\sqrt{3}}{\mathrm{T}}$

• $\frac{\mathrm{\pi a} \sqrt{3}}{2\mathrm{T}}$