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### IITJEE Test Series for SHM

Mulitiple choice questions with one answer

1.The amplitutde and phase of a particle executing SHM depends on
a.The displacemnt of particle at t=0
b.The velocity of particle at t=0
c Both Velocity and displacement at t=0
d Neither velocity and displacemnt at t=0

2.A particle of mass m is attached to a massless string of lenght L and is oscillating in vertical plane with one end of string fixed to rigid support.Tension in the string at a certain instant is T=kmg.Then
a. K can never be equal to 1
b. K can never be greater than 1
c. K can never be greater than 3
d K can never be less than 1

3. A particle is executing SHM at mid point of mean position and extreme position . What is it's KE in terms of total energy E.

(a) E/2
(b) 4E/3
(c) √ 2E
(d) 3E/4

4. A spring of force constant k is cut into two pieces such that one piece is four times the length of the other. the longer piece will have force constant equal to

(a) 4k/5
(b) 5k/4
(c) 3k/2
(d) 4k

5. Total energy of mass spring system in harmonic motion is E=1/2(mω2A2). Consider another system executing SHM with same amplitude having value of spring constant as half the previous one and mass twice as that of previous one. The energy of second oscillator will be

(a) E
(b) 2E
(c) √ 2E
(d) E/2

Mulitiple choice questions with more then one answer

6.For a particle executing SHM
a.Acceleration is proportional to the displacement in the direction of the motion
b.Acceleration is proportional to the displacement but in opposite direction of the motion
c. Total energy of particle remains constant
d KE and PE of particle remains constant

7. which one of the following statement is true
a. Maximum value of velocity in SHM is A2ω
b.In SHM velocity of the particle is maximum when displacment is maximum
c.Velocity of the particle is zero in SHM when displacement attains its maximum on either side
d.Velocity in SHM vary periodically with time

8. which one of the following statement is true
a. Amplitude and intial displacement of particle in SHM are always equal
b.Amplitude and intial displacement of particle in SHM are never equal
c. Amplitnude of a particle in SHM can be equal to its initial displacement
d. Amplitnude of a particle in SHM can be greater to its initial displacement

9.To execute SHM system must have
a. Elasticity
b. Moment of Inertia
c. Inertia
d. all the above

10. Angular frequency of system executing SHM depends on
a. mass
b. total energy
c.force constant
d. Amplitude

Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

11.
STATEMENT 1:Frequency of oscillation in Simple pendulum depends on Amplitude of oscillation
STATEMENT 2:Timeperiod of oscillation in simple pendulum is given by T=2π√L/g

12.
STATEMENT 1:Total energy remains constant in SHM
STATEMENT 2:KE is maximum at mean position

13.
STATEMENT 1:The quantity F.r where F is force and r is displacement is negative in SHM
STATEMENT 2:THe quantity a.r where a is acceleration and r is displacement is positive in SHM

14.
STATEMENT 1:The amplitude or energy is defined by the intial position and intial velocity in SHM
STATEMENT 2:THe phase of motion is determined by the intial position and intial velocity in SHM

MAtrix match type

15.
In a spring mass system executing SHM having mass m and spring constant K with Timeperiod T.Match the column I to the column II

Column I
A) Amplitude is doubled
B) Mass is doubled
C) Spring constant is doubled and mass is 2 doubled also
D)Amplitude is doubled and spring constant is made half

Column II
A) Timeperiod is T
B) Timeperiod is T√2
C) Timeperiod is 2T
D) no match is appropiate

A block of mass M1 resting on the frictionless surface is connected to a spring of spring constant K that is anchored in the nearby wall.A block of mass M2=aM1 is placed on the top of the first block.The coefficent of static friction between the two bodies is μs

16 Assuming the two bodies moves as single object,find the period of oscillation of the system
a T=2π√(1+a)M1/k
b T=2π√M1/k
c. T=2π√(1-a)M1/k
d. None of the above

17. Find the maximum oscillation magnitude Amax that permits the two bodies to move as unit
a. Amax=(1+a)μsgM1/k
b. AmaxsgM1/k
c. AmaxsgM2/k
d. none of the above

18.find the maximum static frictional force on the body M2
a. μsgM1
b. μsgM2
c. μsgaM1
d. none of the above

Solutions