Oscillations's Question 17 | Physics XI - Part 2 | NCERT Exemplar Questions

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MCQ (Multiple Correct Answer)

A body is performing SHM, then its

average total energy per cycle is equal to its maximum kinetic energy

average kinetic energy per cycle is equal to half of its maximum kinetic energy

mean velocity over a complete cycle is equal to $\frac{2}{\pi}$ times of its maximum velocity

root mean square velocity is $\frac{1}{\sqrt{2}}$ times of its maximum velocity

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

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

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

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

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

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.

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.

Subjective

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in figure. When the mass is displaced from equilibrium position by a distance $x$ towards right, find the restoring force.

Explanation

Consider the diagram in which the block is displaced right through x.

The right spring gets compressed by $x$ developing a restoring force $k x$ towards left on the block. The left spring is stretched by an amount $x$ developing a restoring force $k x$ towards left on the block as given in the free body diagram of the block.

$$\begin{aligned} \text { Hence, total force (restoring) } & =(k x+k x) \quad[\because \text { Both forces are in same direction }] \\ & =2 k x \text { towards left } \end{aligned}$$

Subjective

What are the two basic characteristics of a simple harmonic motion?

Explanation

The two basic characteristics of a simple harmonic motion

(i) Acceleration is directly proportional to displacement.

(ii) The direction of acceleration is always towards the mean position, that is opposite to displacement.

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