Objective Question for SHM

Q 1. 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

Q 2. A particle is executing linear SHM of amplitude A. What fraction of total energy is potential when the displacement is 1/4 times amplitude.

(a) 3/2
(b) 1/16
(c) 1/4
(d) 1/2√ 2

Q 3. Fig below shows two spring mass systems. All the springs are identical having spring constant k and are of negligible mass. If m is the mass of block attached to the spring then the ratio of time period of oscillations of both systems is

(a) 1:2√ 2
(b) 1:1/2√ 2
(c) 1:√ 2
(d) √ 2:1

Q 4. Fig below shows two equal masses of mass m joined by a rope passing over a light pully. First mass is attached to a spring and another end of spring is attached to a rigid support. Neglacting frictional forces total energy of the system when spring is extended by a distance x is

(a) mv2+1/2(Kx2)+mgx
(b) mv2-1/2(Kx2)+mgx
(c) mv2-1/2(Kx2)-mgx
(d) mv2+1/2(Kx2)-mgx

where v = dx/dt , the velocity of mass

Q 5. 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

Q 6. In the system shown below frequency of oscillation when mass is displaced slightely is

(a) f=1/2π(k1k2/(k1+k2)m)1/2
(b) f=1/2π((k1+k2)/m)1/2
(c) f=1/2π(m/(k1k2))1/2
(d) f=1/2π((k1+k2)/(k1k2)m)1/2

Q 7. A simple pendulum is displaced from it's mean position o to a position A such that hight of A above O is 0.05m. It is then released it's velocity when it passes mean position is

(a) .1m/s
(b) 5.0m/s
(c) 1m/s
(d) 1.5m/s

Q 8. 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

Q 9. A solid cylinder of radius r and mass m is connected to a spring of spring constant k and it slips on a frictionless surface without rolling with angular frequency

(a) √(k/mr)
(b) √(kr/m)
(c) √(k/m)
(d) √(2k/m)


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