A particle is executing two different simple harmonic motions, mutually perpendicular, of different amplitudes and having a phase difference of π/2. The path of the particle will be :

• circular

• straight line

• parabolic

• elliptical

Equations of motion in the same direction are given by :

y₁ = 2a sin(ωt - kx)

y₂ = 2a sin(ωt - kx - θ)

The amplitude of the medium particle will be:

• 2a cosθ

• $\sqrt{2}$ a cosθ

• 4 a cos$\frac{\mathrm{\theta }}{2}$

• $\sqrt{2}\mathrm{a} \cos \frac{\mathrm{\theta }}{2}$

To make the frequency double of a spring oscillator, we have to :

• reduce the mass to one fourth

• quadruple the mass

• double the mass

• half the mass

214.

A particle executing SHM has amplitude 0.01 m and frequency 60 Hz. The maximum acceleration of the particle is :

• $60{\mathrm{\pi }}^2 \mathrm{m}/{\mathrm{s}}^2$

• $80{\mathrm{\pi }}^2 \mathrm{m}/{\mathrm{s}}^2$

• $120{\mathrm{\pi }}^2 \mathrm{m}/{\mathrm{s}}^2$

• $144{\mathrm{\pi }}^2 \mathrm{m}/{\mathrm{s}}^2$

When a wave travels in a medium, the particle's displacement is given by the equation

y = 0.03 sin(2t - 0.01 x)

where x and y are in metre and t in second. The wavelength of the wave is :

• 200 m

• 100 m

• 20 m

• 10 m

The false statement is

• Every SHM is periodic in nature

• Every periodic motion is SHM

• In every SHM, total energy is proportional to the square of amplitude

• In SHM, acceleration of oscillating body is proportional to the displacement from the equilibrium position

Two pendulums of lengths 100 cm and 121 cm start vibrating. At some instant the two are at the mean position in the same phase. After how many vibrations of the longer pendulum will the two be in the same phase at the mean position again?

• 10

• 11

• 20

• 21

A child swinging on a swing in sitting position, stands up, then the time period of swing will

• increase

• decrease

• remain same

• increase if the child is long and decrease if the child is short

A mass of 10 g moving horizontally with a velocity of 100 cm/s strikes a pendulum bob of mass 10 g. The two masses stick together. The maximum height reached by the system now is (g = 10 m/s²)

• zero

• 5 cm

• 2.5 cm

• 1.25 cm

A particle of mass 10 g is executing simple harmonic motion with an amplitude of 0.5 m and periodic time of ($\mathrm{\pi }$/ 5) second. The maximum value of the force acting on the particle is

• 25 N

• 5 N

• 2.5 N

• 0.5 N