This document contains questions that may be asked about the topic of oscillation. It includes questions ranging from 1 to 4 marks testing a variety of concepts. Some of the key concepts that could be assessed include: defining terms related to simple harmonic motion such as period, amplitude, phase; deriving expressions for kinetic energy, potential energy, and total energy of a particle in SHM; representing displacement, velocity and acceleration graphs for SHM; obtaining differential equations of motion for various oscillatory systems; and analyzing composition of two SHMs. The document also provides important formulas that may be used to answer oscillation questions.

1. Oscillation
Total marks 5/7
Possible questions may be of
1,2,3 or 4 marks

2. 2 marks question
Define
1. Periodic motion, Linear SHM
2. Phase of a particle performing SHM
3. Amplitude, Period for particle in SHM
4. Angular SHM, force constant
5. Phase and epoch
6. Second’s pendulum, simple pendulum
7. State the expression for KE and write values
for KE at mean position and extreme position

3. 8. Show that PE of a particle is directly
proportional to the square of its displacement
from mean position
9. Assuming expression for KE and PE of a
particle performing SHM obtain expression
for TE and deduce conclusion from it.
10.Define second’s pendulum and show that
length of seconds pendulum is constant at
given place
11.Deduce an expression for period of a particle
performing SHM in terms of force constant
12.Draw diagram showing displacement and
velocity against time

4. 13.Obtain expression of velocity using
differential equation of SHM
14.Obtain expression for period of
simple pendulum
15. State differential equation for
angular SHM give one example for
the same.
16. Represent KE and PE against
displacement in separate graphs with
proper labeling

5. 13.Write down at what distance from
mean position the KE =PE and at
what distance velocity will be half of
maximum
14.The solution of equation representing
the motion of block under damping
force which is proportional to velocity
and expression for period is ?
15.Write the expression for amplitude of
damped oscillation and explain effect
of time on amplitude.

6. 3 marks question
16. Show that linear SHM can be considered as the
projection of UCM on any diameter
17. Represent graphically the displacement, velocity
and acceleration against time for a particle
performing linear SHM when it starts from extreme
position
18. Assuming general equation of displacement in SHM
obtain expression for velocity and acceleration
19. Obtain expressions for KE,PE and hence show that
TE is constant for linear SHM
20. Discuss analytically, the composition of two SHMs
of same period and parallel to each other

7. 4 marks question
21.State the differential equation of SHM and
obtain expression for displacement, velocity
and acceleration
22.Obtain expression for period of simple
pendulum, hence calculate the length of
second’s pendulum
23.Obtain expression for the period of a magnet
vibrating in a uniform magnetic induction
24.If x1 = a1sin(t+1) and x2=a2sin(t + 2)
obtain an expression for resultant amplitude
hence obtain resultant amplitude when
phase differ by 0o and by 90o.

8. 4 marks question
25.What is damped oscillation, obtain
differential equation of damped oscillation if
damping force is proportional to velocity.
26.Obtain expression for period of simple
pendulum, hence calculate the length of
second’s pendulum
27.Obtain expression for the period of a magnet
vibrating in a uniform magnetic induction
28.If x1 = a1sin(t+1) and x2=a2sin(t + 2)
obtain an expression for resultant amplitude
hence obtain resultant amplitude when
phase differ by 0o and by 90o.

9. Important formulae of Oscillation
xω-x
m
k
dt
xd 2
2
2

)Asin(x   t
22
xA)cos(AV   t
xt 22
 )sin(A-a 
)x-k(A
2
1
)x-(Am
2
1
KE 2222
 2

22
kx
2
1
xm
2
1
PE  2
 22
kA
2
1
Am
2
1
TE  2


10. Important formulae of Oscillation
ntdisplacemeunitperacc.
1
2π
k
m
2πT 
2
g
L2,Tpendulumssecond'for


pendulumsimpleT
g
L
2
magnetbar
MB
I
T 2

11. Important formulae of Oscillation
2
2
d x dx
m b kx 0
dtdt
  
2k b
' ( )
m 2m
  
bt
2m
x Ae cos( 't )

   
2
2
T
k b
( )
m 2m




12. ElasticityTotal Marks 4/6
Possible questions are of
1,2,3 or 4 marks

13. Questions of 2 marks
1. What is elasticity? How can you differentiate
between elastic body and plastic body?
2. Define deforming force and perfectly elastic body
3. Define stress and strain, write their units
4. Define stress, strain and their dimension
5. What is shearing stress? State its units and
dimension
6. The graph of stress against strain
is as shown in adjoining figure,
state what points E,Y and C
represents, define any one of them

14. 7. Define bulk modulus & derive expression
for it.
8. What is elastic limit? What happens
beyond elastic limit?
9. State Hooks law of elasticity and define
modulus of elasticity
10.Explain why only solids posses all the
three constants of elasticity
11.Deduce an expression of Young’s
modulus of material of a long uniform wire

15. 13.Assuming Hook’s law show that Young’s
modulus of the material of a wire is the
stress required to double the length of
wire
14.Define modulus of rigidity and derive its
necessary formula
15.Prove that deforming force is directly
proportional to the change in the volume
of a wire in the case of Young’s modulus

16. 16.Define Yield point, Breaking point
17.Explain why two identical wires of the
same material used in method for the
determination of Y
18.Define “ Elastometers” ( elastomers).
Draw stress – strain curve for an
elastomer.
19.Obtain relation between Young’s modulus
and coefficient of linear expansion.
20.Write down the expression for sag and
explain terms used in it.

17. Questions for 3 marks
21.Define strain and explain its different types
22. What is Poisson’s ratio? Why it does not
have any unit?
23.Give the expression of sag of horizontal
beam and explain terms used in it.
24.How will you relate ductility and brittleness
with stress strain graph. Give examples of
both types.
25.Define thermal stress and relate it with
coefficient of linear expansion and Young’s
modulus.

18. Questions for 4 marks
26.Derive expression for work done per unit
volume in stretching a wire
27.With the graph explain behavior of a wire
under increasing load
28.Prove that strain energy per unit volume
equals (stress x strain)/2

19. Important formulae
xrπ
LgM
x
L
A
F
Y 2

Yrπ
LgM
x 2

dV
VdP
)
V
V(
dP
K 




A
F

Dx
dL
L
x
D
d

)(
)(

2
22
2
1
2
1
2
1
2
 


kF
)strss(
Y
)strain(
Y
)strain()stress(
2
1
W
3
3
WL
4bd Y
 
Thermal Stress = Y ( ) 