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Physics. Session. Simple Harmonic Motion - 2. Session Objectives. Session Objective. Angular SHM. Pendulum (Simple). Torsional Pendulum. Horizontal Vibration of a spring. Vertical Vibration of a spring. Combination of springs in series. Combination of springs in Parallel. Angular SHM.

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session

Session

Simple Harmonic Motion - 2

session objective
Session Objective

Angular SHM

Pendulum (Simple)

Torsional Pendulum

Horizontal Vibration of a spring

Vertical Vibration of a spring

Combination of springs in series

Combination of springs in Parallel

horizontal vibrations of spring
Horizontal Vibrations of Spring

Same result holds good for vertical vibrations of a spring also.

solution
Solution

a) The two springs are in parallel so

b) The springs are in parallel so

class exercise 1

The appropriate graph between time period T of angular SHM of a body and radius of gyration r is

(a) (b)

(c) (d)

Class Exercise - 1
solution1
Solution

Hence, answer is (a).

solution2

So (a).

and So (b).

Solution

All others are wrong except these.

Hence, answer is (a) & (b).

class exercise 3
Class Exercise - 3

A hollow metallic bob is filled with water and hung by a long thread. A small hole is drilled at the bottom through which water slowly flows out. The period of oscillations of sphere

(a) decreases(b) increases(c) remains constant(d) first increases and then decreases

solution3
Solution

As the water slowly flows out, the centre of gravity moves down. So the length increases and hence T increases. After half the sphere is empty, the centre of gravity begins to move up. So the length decreases and hence T decreases.

Hence, answer is (d).

class exercise 4

The total energy of a simple pendulum is E. When the displacement is half of amplitude, its kinetic energy will be

(a) E (b) (c) (d)

Class Exercise - 4
solution4

Now

Solution

Hence, answer is (b).

class exercise 5

A spring has a spring constant K. It is cut into two equal lengths and the two cut pieces are connected in parallel. Then the spring constant of the parallel combination is(a) K(b)2K(c) 4K (d)

Class Exercise - 5
solution5
Solution

Spring constant of cut pieces

K´ = 2K

Now parallel combination of these results in a spring constant.

= 4K

Hence, answer is (c).

class exercise 6

A spring of spring constant K is divided into nine equal parts. The new spring constant of each part is

(a) 9K (b)(c) 3K (d)

Class Exercise - 6
solution6

If force is constant, then

Now let K´ be new spring constant. Then

Solution

We know that for springF = Kx

or K´ = 9K

Hence, answer is (a).

class exercise 7

The amplitude of damped oscillator becomes one-half after t seconds.If the amplitude becomes after3tseconds, then n is equal to(a) (b) 8(c) (d) 4

Class Exercise - 7
solution7
Solution

Hence, n = 8

Hence, answer is (a).

class exercise 8

The angle f at which the mean position exists of a simple pendulum placed in acar accelerating by to right is

(a) (b)

(c) (d) None of these

Class Exercise - 8
solution8
Solution

T cosf = mg

Hence, answer is (a).

class exercise 9

Keg of following figure is

(a) K1 + K2 + K3 + K4(b)

(c)(d) None of these

Class Exercise - 9
solution9
Solution

When we displace the body from its mean position, we see the extension in all the springs is same. So the combination is parallel.

Hence answer is (a).

class exercise 10

What is the resultant time period of a particle, if following two SHMs in same direction when superimposed on each other is x1 = Asinwt, x2 = Acoswt?

(a) (b)

(c) (d) None of these

Class Exercise - 10
solution10

So the time period =

Solution

X = X1 + X2

= A sinwt + A coswt

Hence, answer is (a).