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# Physics - PowerPoint PPT Presentation

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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## Physics

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Presentation Transcript

### Session

Simple Harmonic Motion - 2

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

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

Solution

a) The two springs are in parallel so

b) The springs are in parallel so

• K b. 2K
• c. 4K d.

2K

K

K

Illustrative Problem

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
Solution

(a) (b)

(c) (d)

Class Exercise - 2

So (a).

and So (b).

Solution

All others are wrong except these.

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

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

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.

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

Now

Solution

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
Solution

Spring constant of cut pieces

K´ = 2K

Now parallel combination of these results in a spring constant.

= 4K

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

If force is constant, then

Now let K´ be new spring constant. Then

Solution

We know that for springF = Kx

or K´ = 9K

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
Solution

Hence, n = 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
Solution

T cosf = mg

Keg of following figure is

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

(c)(d) None of these

Class Exercise - 9
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.

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

So the time period =

Solution

X = X1 + X2

= A sinwt + A coswt