TextBook Solutions for Goa Board of Secondary and Higher Secondary Education Class 11 Physics Physics Part Ii Chapter 14 Oscillations

If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

• a²T²+ 4π²v²

• aT/x

• aT + 2πv

• aT/v 

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance.Then 

• 18 > x

• x >54

• 54 > x > 36 

• 36 > x > 18

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10^-2 cos πt metres. The time at which the maximum speed first occurs

• 0.5 s

• 0.75 s

• 0.125 s

• 0.325 s

A point mass oscillates along the x-axis according to the law x = x₀ cos (ωt - π/4). If the acceleration of the particle is written as a = A cos (ωt + δ), then

• A = x₀ , δ = – π/4

• A = x₀ ω₂ , δ = π/4 

• A = x₀ ω₂, δ = –π/4 

• A = x₀ ω2, δ = 3π/4

Two springs, of force constants _k1 and k₂, are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both k₁ and k₂ are made four times their original values, the frequency of oscillation becomes

• f/2

• f/4

• 4f

• 2f

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

• 2π²ma²v²

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

• 0.1 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

• 1/4s

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 g2/ 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 π/ω.