A particle of mass m executes simple harmonic motion with amplitude ‘a’ and frequency ‘ν’. The average kinetic energy during its motion from the position of equilibrium to the end is

• π²m a² v²

• ma² v²/4

• 4π²ma²v²

• 4π²ma²v²

22.

The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is

• 100 s

• 0.01 s

• 10 s

• 10 s

Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy?

• 1/6s

• 1/12s

• 1/3s

• 1/3s

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

• at the highest position of the platform

• at the mean position of the platform

• for an amplitude of g/ω² 

• for an amplitude of g/ω² 

The function sin²(ωt) represents

• a periodic, but not simple harmonic motion with a period 2π/ω

• a periodic, but not simple harmonic motion with a period π/ω

• a simple harmonic motion with a period 2π/ω

• a simple harmonic motion with a period 2π/ω

Two simple harmonic motions are represented by the equation y₁ = 0.1  and y₂ = 0.1 cosπt. The phase difference of the velocity of particle 1 w.r.t. the velocity of the particle 2 is

• −π/6

• π/3

• −π/3

• −π/3

If a simple harmonic motion is represented by , its time period is its time period

• 2π/α

• 

• 2πα

• 2πα

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

• first increase and then decrease to the original value.

• first decreased then increase to the original value.

• remain unchanged.

• remain unchanged.

The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t0 in the air. Neglecting frictional force of water and given that the density of the bob is (4/3) x 1000 ms^-1 . What relationship between t and t0 is true?

• t = t₀

• t = t₀/2

• t = 2t₀

• t = 2t₀

A particle at the end of a spring executes simple harmonic motion with a period t₁, while the corresponding period for another spring is t₂. If the period of oscillation with the two springs in series is t, then

• T = t₁ + t₂

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