Question

. Choose the correct option.

i) A particle performs linear S.H.M.

starting from the mean position. Its

amplitude is A and time period is T. At

the instance when its speed is half the

maximum speed, its displacement x is

(A) 3

2

A (B)

2

3

A

(C) A

2 (D) 1

2

A

ii) A body of mass 1 kg is performing linear

S.H.M. Its displacement x (cm) at t

(second) is given by

x = 6 sin (100t + π/4). Maximum kinetic

energy of the body is

(A) 36 J (B) 9 J

(C) 27 J (D) 18 J

iii) The length of second's pendulum on the

surface of earth is nearly 1 m. Its length

on the surface of moon should be [Given:

acceleration due to gravity (g) on moon

is 1/6 th of that on the earth’s surface]

(A) 1/6 m (B) 6 m

(C) 1/36 m (D) 1

6

m

iv) Two identical springs of constant k are

connected, first in series and then in

parallel. A metal block of mass m is

suspended from their combination. The

ratio of their frequencies of vertical

oscillations will be in a ratio

(A) 1:4 (B) 1:2 (C) 2:1 (D) 4:1

v) The graph shows variation of

displacement of a particle performing

S.H.M. with time t. Which of the

following statements is correct from the

graph?

(A) The acceleration is maximum at

time T.

(B) The force is maximum at time 3T/4.

(C) The velocity is zero at time T/2.

(D) The kinetic energy is equal to total

energy at time T/4.

Exercises

2. Answer in brief.

i) Define linear simple harmonic motion.

ii) Using differential equation of linear

S.H.M, obtain the expression for (a)

velocity in S.H.M., (b) acceleration in

S.H.M.

iii) Obtain the expression for the period of a

simple pendulum performing S.H.M.

iv) State the laws of simple pendulum.

v) Prove that under certain conditions a

magnet vibrating in uniform magnetic

field performs angular S.H.M.

3. Obtain the expression for the period of a

magnet vibrating in a uniform magnetic

field and performing S.H.M.

4. Show that a linear S.H.M. is the

projection of a U.C.M. along any of its

diameter.

5. Draw graphs of displacement, velocity

and acceleration against phase angle,

for a particle performing linear S.H.M.

from (a) the mean position (b) the

positive extreme position. Deduce your

conclusions from the graph.

6. Deduce the expressions for the kinetic

energy and potential energy of a particle

executing S.H.M. Hence obtain the

expression for total energy of a particle

performing S.H.M and show that the

total energy is conserved. State the

factors on which total energy depends.

7. Deduce the expression for period of

simple pendulum. Hence state the factors

on which its period depends.

8. At what distance from the mean position

is the speed of a particle performing

S.H.M. half its maximum speed. Given

path length of S.H.M. = 10 cm.

[Ans: 4.33 cm]​

Answer 1

Answer:

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Explanation:

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