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
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
D.
4f