The displacement of a particle varies with time according to the relation

y = a sin ωt + b cos ωt.

A. The motion is oscillatory but not S.H.M.

B. The motion is S.H.M. with amplitude a + b.

C. The motion is S.H.M. with amplitude a² + b².

D. The motion is S.H.M. with amplitude √ a² + b².

A travelling wave is produced on a long horizontal string by vibrating and end up and down sinusoidally. The amplitude of vibration is 10 cm and the displacement becomes zero 200 times per second. The linear mass density of the string is 010 kg m⁻¹ and it is kept under a tension of 90 N. (A) Find the speed and the wavelength of the wave. (B) Assume that the wave moves in the position x-direction and at t = 0, the end x = 0 is at its positive extreme position. Write the wave equation. (C) Find the velocity and acceleration of the particle at x = 50 cm at time t = 10 ms.

Displacement vs. time curve for a particle executing S.H.M. is shown in Fig. 14.4. Choose the correct statements.

Four pendulums A, B, C and D are suspended from the same

elastic support as shown in Fig. 14.1. A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse displacement,

The displacement of a particle varies with time according to the relation

y = a sin ωt + b cos ωt.

The rotation of earth about its axis is

A wave travelling on a string at a speed of 10 m s⁻¹ causes each particle of the string to oscillate with a time period of 20 ms. (A) What is the wavelength of the wave? (B) If the displacement of a particle is 15 mm at a certain instant, what will be the displacement of a particle 10 cm away from it at the same instant?

Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is

Figure 14.2. shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is

Figure (15-E2) shows a plot of the transverse displacements of the particles of a string at t = 0 through which a travelling wave is passing in the positive x-direction. The wave speed is 20 cm s⁻¹. Find (A) the amplitude, (B) the wavelength, (C) the wave number and (D) the frequency of the wave.

Two particles A and B have a phase difference of π when a sine wave passes through the region.