Simple Harmonic...

Four pendulums A, B, C and D are suspended from the same elastic support as shown in figure. 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 equation of motion of a particle is x = acos(αt)². The motion is

Which of the following statements is/are true for a simple harmonic oscillator?

a. Force acting is directly proportional to displacement from the mean position and opposite to it

b. Motion is periodic

c. Acceleration of the oscillator is constant 

d. The velocity is periodic

The displacement time graph of a particle executing SHM is shown in the figure. Which of the following statement is/are true?

a) the force is zero at t = 3T/4

b) the acceleration is maximum at t = 4T/4

c) the velocity is maximum at t = T/4

d) the PE is equal to KE of oscillation t = T/2

A particle is in linear simple harmonic motion between two points A and B, 10 cm apart (figure.) Take the direction from A to B as the positive direction and choose the correct statements.

AO=OB=5 cm

BC= 8 cm

a. The sign of velocity, acceleration and force on the particle, when it is 3 cm away from A going towards B, are positive.

b. The sign of velocity of the particle at C going towards B is negative.

c. The sign of velocity, acceleration and force on the particle, when it is 4 cm away from B going towards A, are negative.

d. The sign of acceleration and force on the particle when it is at points B is negative.

The rotation of the earth about its axis is:

a. periodic motion

b. simple harmonic motion

c. periodic but not simple harmonic motion

d. non-periodic motion

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

a. simple harmonic motion

b. non-periodic motion

c. periodic motion

d. periodic but not SHM

From the given functions, identify the function which represents a periodic motion:

On average, a human heart is found to beat 75 times in a minute. Its frequency and period respectively are:

Which of the following functions of time represent/s periodic motion? [ω is any positive constant]

(a) sinωt + cosωt

(b) sinωt + cos2ωt + sin4ωt

(c) e^–ωt

(d) log(ωt)

(e) sin²ωt