Two particles are executing simple harmonic motion of the same amplitude Aand frequency ω along the x - axis. Their mean position is separated by distance X₀ (X₀ >A). If the maximum separation between them is (X0 + A), the phase difference between their motion is

• π/3

• π/4

• π/6

• π/6

A mass M, attached to a horizontal spring, executes SHM with an amplitude A₁. When the mass M passes through its mean position than a smaller mass m is placed over it and both of them move together with amplitude A₂. The ratio of (A₁/A₂) is

The equation of a wave on a string of linear mass density 0.04 kg m^–1 is given by y= 0.02(m) sin  The tension in the string is 

• 4.0 N

• 12.5

• 0.5 N

• 0.5 N

A particle is executing simple harmonic motion with a time period T. AT time t = 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like 

A magnetic needle of magnetic moment 6.7 × 10^–2 Am² and moment of inertia 7.5 × 10^–6 kg m² is performing simple harmonic oscillations in a magnetic field of 0.01 T.Time taken for 10 complete oscillations is :

• 6.98 s 

• 8.76 s

• 6.65 s

• 6.65 s

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 + 2πv

17.

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 

• 54 > x > 36 

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

• 0.125 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 = –π/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

• 4f