Which of the following functions represents a simple harmonic oscillation?

• sinωt $-$ cosωt

• sin²ωt

• sinωt + sin2ωt

• sinωt $-$ sin2ωt

A magnet is made to oscillate with a particular frequency, passing through a coil as shown in figure. The time variation of the magnitude of e.m.f. generated across the coil during one cycle is

Assertion: The amplitude of an oscillating pendulum decreases gradually with time. 

Reason: The frequency of the pendulum decreases with time.

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

• if both assertion and reason are true and the reason is not the correct explanation of the assertion

• if assertion is true but reason is false

• if both assertion and reason are false statements

A string in a musical instrument is 50 cm long and its fundamental frequency is 800 Hz. If a frequency of  1000 Hz is to be produced, then required length of string is

• 62.5 cm

• 40 cm

• 50 cm

• 37.5 cm

Assertion:  The time-period of pendulum, on a satellite orbiting the earth is infinity. 

Reason:  Time-period of a pendulum is inversely  proportional to  $\sqrt{\mathrm{g}}$

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

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

• If the assertion is true but the reason is false.

• If both assertion and reason are false.

Assertion: In simple harmonic motion, the motion is  to and fro and periodic.

Reason: Velocity of the particle  ( v)  = ω$\sqrt{{\mathrm{k}}^2 - {\mathrm{x}}^2}$ ( where x is the displacement ).

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

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

• If the assertion is true but the reason is false.

• If both assertion and reason are false.

The time period of a simple pendulum is T remaining at rest inside a lift. Find the time period of pendulum when lift starts to move up with an acceleration of  g/4

• T

• T/2

• $\frac{2\mathrm{T}}{5}$

• $\frac{2\mathrm{T}}{\sqrt{5}}$

From the given figure find the  frequency of oscillation of the mass m. 

A simple pendulum is made by attaching a 1 kg bob to a 5 m long copper wire. Its period is T. Now, if 1 kg bob is replaced by 10 kg bob, the period of oscillations

• remains T

• becomes greater than T

• becomes less than T

• any of the above depends on gravity

The length of a second's pendulum is

• 99.8 cm

• 99 cm

• 100 cm

• None of the above