DPP-1
UDAAN
Simple Harmonic Motion EXCLUSIVE
1. In a simple harmonic oscillator, at the mean position:
(1) kinetic energy is minimum, potential energy is maximum DPP
(2) both kinetic and potential energies are maximum
(3) kinetic energy is maximum, potential energy is minimum
(4) both kinetic and potential energies are minimum
2. A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so
that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes 5T/
3. Then the ratio of m/M is :
(1) 3/5 (2) 25/9 (3) 16/9 (4) 5/3
3. The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage
increase in the time period of the pendulum of increased length is :
(1) 11% (2) 21% (3) 42% (4) 10%
4. The displacement of a particle varies according to the relation x = 4 (cos t + sin t). The amplitude of the
particle is :
(1) –4 (2) 4 (3) 4 2 (4) 8
5. A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total
energy (T.E.) are measured as function of displacement x. Which of the following statements is true?
(1) K.E. is maximum when x = 0 (2) T.E. is zero when x = 0
(2) K.E. is maximum when x is maximum (4) P.E. is maximum when x = 0
6. A simple pendulum is executing simple harmonic motion with a time period T. If the length of the pendulum
is increased by 21%, the % increase in the time period of the pendulum of increased length is-
(1) 10% (2) 21% (3) 30% (4) 50%
7. The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of
oscillation of the bob is t0 in air. Neglecting frictional force of water and given that the density of the bob is
(4/3) × 1000 kg/m3. What relationship between t and t0 is true?
(1) t = t0 (2) t = t0/2 (3) t = 2t0 (4) t = 4t0
8. A particle at the end of a spring executes simple harmonic motion with a period t1, while the corresponding
period for another spring is t2. If the period of oscillation with the two springs in series is T, then :
(1) T = t1 + t2 (2) T2 = t12 + t22 (3) T–1 = t1–1 + t2–1 (4) T–2 = t1–2 + t2–2
9. The total energy of a particle, executing simple harmonic motion is :
(1) x (2) x2 (3) independent of x (4) x1/2
Where x is the displacement from the mean position.
10. A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency 0. An
external force F(t) proportional to cos t ( 0) is applied to the oscillator. The time displacement of the
oscillator will be proportional to :
m 1 1 m
(1) (2) (3) (4)
20 2
m ( 20 2
) m ( 20 2
) 20 2
11. In forced oscillation of a particle, the amplitude is maximum for a frequency 1 of the force, while the energy
is maximum for a frequency 2 of the force, then :
(1) 1 = 2
(2) 1 > 2
(3) 1 < 2 when damping is small and 1 > 2 when damping is large
(4) 1 < 2
Page # 1
, d2 x
12. If a simple harmonic motion is represented by + x = 0, its time period is :
dt 2
2 2
(1) (2) (3) 2 (4) 2
13. The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the
oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of
oscillation would :
(1) first increase and then decrease to the original value
(2) first decrease and then increase to the original value
(3) remain unchanged
(4) increase towards a saturation value
14. The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s.
The period of oscillation is :
(1) 100 s (2) 0.01 s (3) 10 s (4) 0.1 s
15. A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular fre-
quency .The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for
the first time :
(1) at the highest position of the platform (2) at the mean position of the platform
g g2
(3) for an amplitude of (4) for an amplitude of
2 2
16. The displacement of an object attached to a spring and executing simple harmonic motion is given by
x = 2 × 10–2 cost metres. The time at which the maximum speed first occurs is :
(1) 0.5 s (2) 0.75 s (3) 0.125 s (4) 0.25 s
17. A point mass oscillates along the x-axis according to the law x = x0 cos (t – /4). If the acceleration of the
particle is written as , a = A cos(t + ), then :
(1) A = x0 , = –/4 (2) A = x02, = –/4 (3) A = x02, = –/4 (4) A = x02, = 3/4
18. Two springs, of force constants k1 and k2, are connected to a mass m as shown. The frequency of oscillation
of mass is ƒ. If both k1 and k2 are made four times their original values, the frequency of oscillation becomes:
(1) ƒ/2 (2) ƒ/4 (3) 4f (4) 2ƒ
19. A particle of mass m executes simple harmonic motion with amplitude a and frequency . The average
kinetic energy during its motion from the position of equilibrium to the end is :
1
(1) 2 ma2 2 (2) ma2 2 (3) 42 ma2 2 (4) 22 ma22
4
20. If x,v and a denote the displacement, the velocity and the acceleration of a particle executing simple har-
monic motion of time period T, then, which of the following does not change with time?
aT aT
(1) (2) aT + 2v (3) (4) a2T2 + 42v2
x v
Page # 2
UDAAN
Simple Harmonic Motion EXCLUSIVE
1. In a simple harmonic oscillator, at the mean position:
(1) kinetic energy is minimum, potential energy is maximum DPP
(2) both kinetic and potential energies are maximum
(3) kinetic energy is maximum, potential energy is minimum
(4) both kinetic and potential energies are minimum
2. A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so
that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes 5T/
3. Then the ratio of m/M is :
(1) 3/5 (2) 25/9 (3) 16/9 (4) 5/3
3. The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage
increase in the time period of the pendulum of increased length is :
(1) 11% (2) 21% (3) 42% (4) 10%
4. The displacement of a particle varies according to the relation x = 4 (cos t + sin t). The amplitude of the
particle is :
(1) –4 (2) 4 (3) 4 2 (4) 8
5. A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total
energy (T.E.) are measured as function of displacement x. Which of the following statements is true?
(1) K.E. is maximum when x = 0 (2) T.E. is zero when x = 0
(2) K.E. is maximum when x is maximum (4) P.E. is maximum when x = 0
6. A simple pendulum is executing simple harmonic motion with a time period T. If the length of the pendulum
is increased by 21%, the % increase in the time period of the pendulum of increased length is-
(1) 10% (2) 21% (3) 30% (4) 50%
7. The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of
oscillation of the bob is t0 in air. Neglecting frictional force of water and given that the density of the bob is
(4/3) × 1000 kg/m3. What relationship between t and t0 is true?
(1) t = t0 (2) t = t0/2 (3) t = 2t0 (4) t = 4t0
8. A particle at the end of a spring executes simple harmonic motion with a period t1, while the corresponding
period for another spring is t2. If the period of oscillation with the two springs in series is T, then :
(1) T = t1 + t2 (2) T2 = t12 + t22 (3) T–1 = t1–1 + t2–1 (4) T–2 = t1–2 + t2–2
9. The total energy of a particle, executing simple harmonic motion is :
(1) x (2) x2 (3) independent of x (4) x1/2
Where x is the displacement from the mean position.
10. A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency 0. An
external force F(t) proportional to cos t ( 0) is applied to the oscillator. The time displacement of the
oscillator will be proportional to :
m 1 1 m
(1) (2) (3) (4)
20 2
m ( 20 2
) m ( 20 2
) 20 2
11. In forced oscillation of a particle, the amplitude is maximum for a frequency 1 of the force, while the energy
is maximum for a frequency 2 of the force, then :
(1) 1 = 2
(2) 1 > 2
(3) 1 < 2 when damping is small and 1 > 2 when damping is large
(4) 1 < 2
Page # 1
, d2 x
12. If a simple harmonic motion is represented by + x = 0, its time period is :
dt 2
2 2
(1) (2) (3) 2 (4) 2
13. The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the
oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of
oscillation would :
(1) first increase and then decrease to the original value
(2) first decrease and then increase to the original value
(3) remain unchanged
(4) increase towards a saturation value
14. The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s.
The period of oscillation is :
(1) 100 s (2) 0.01 s (3) 10 s (4) 0.1 s
15. A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular fre-
quency .The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for
the first time :
(1) at the highest position of the platform (2) at the mean position of the platform
g g2
(3) for an amplitude of (4) for an amplitude of
2 2
16. The displacement of an object attached to a spring and executing simple harmonic motion is given by
x = 2 × 10–2 cost metres. The time at which the maximum speed first occurs is :
(1) 0.5 s (2) 0.75 s (3) 0.125 s (4) 0.25 s
17. A point mass oscillates along the x-axis according to the law x = x0 cos (t – /4). If the acceleration of the
particle is written as , a = A cos(t + ), then :
(1) A = x0 , = –/4 (2) A = x02, = –/4 (3) A = x02, = –/4 (4) A = x02, = 3/4
18. Two springs, of force constants k1 and k2, are connected to a mass m as shown. The frequency of oscillation
of mass is ƒ. If both k1 and k2 are made four times their original values, the frequency of oscillation becomes:
(1) ƒ/2 (2) ƒ/4 (3) 4f (4) 2ƒ
19. A particle of mass m executes simple harmonic motion with amplitude a and frequency . The average
kinetic energy during its motion from the position of equilibrium to the end is :
1
(1) 2 ma2 2 (2) ma2 2 (3) 42 ma2 2 (4) 22 ma22
4
20. If x,v and a denote the displacement, the velocity and the acceleration of a particle executing simple har-
monic motion of time period T, then, which of the following does not change with time?
aT aT
(1) (2) aT + 2v (3) (4) a2T2 + 42v2
x v
Page # 2
