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15
MCQ (Multiple Correct Answer)

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
16
MCQ (Multiple Correct Answer)

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

A
The force is zero at $t=\frac{3 T}{4}$
B
The acceleration is maximum at $t=\frac{4 T}{4}$
C
The velocity is maximum at $t=\frac{T}{4}$
D
The PE is equal to KE of oscillation at $t=\frac{T}{2}$
17
MCQ (Multiple Correct Answer)

A body is performing SHM, then its

A
average total energy per cycle is equal to its maximum kinetic energy
B
average kinetic energy per cycle is equal to half of its maximum kinetic energy
C
mean velocity over a complete cycle is equal to $\frac{2}{\pi}$ times of its maximum velocity
D
root mean square velocity is $\frac{1}{\sqrt{2}}$ times of its maximum velocity
18
MCQ (Multiple Correct Answer)

A particle is in linear simple harmonic motion between two points. $A$ and $B, 10 \mathrm{~cm}$ 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
19
Subjective

Displacement versus time curve for a particle executing SHM is shown in figure. Identify the points marked at which (i) velocity of the oscillator is zero, (ii) speed of the oscillator is maximum.

Displacement versus time curve for a particle executing SHM is shown in figure. Identify the points marked at which (i) velocity of the oscillator is zero, (ii) speed of the oscillator is maximum.

Explanation

In SHM y-t graph, zero displacement values correspond to mean position; where velocity of the oscillator is maximum.

Whereas the crest and troughs represent extreme positions, where displacement is maximum and velocity of the oscillator is minimum and is zero. Hence,

(a) $A, C, E, G$ are either crest or trough having zero velocity.

(b) speed is maximum at mean positions represented by $B, D, F, H$ points.

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