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Practice each question, then open the answer or worked solution.
When a mass m is connected individually to two springs S1 and S2, the oscillation frequencies are v1 and v2. If the same mass is attached to the two springs are shown in the figure, the oscillation frequency would be
a) v1 + v2
b)
c)
d)
The correct answer b)
The rotation of the earth about its axis is
a) periodic motion
b) simple harmonic motion
c) periodic but not simple harmonic motion
d) non-periodic motion
The correct answers are
a) periodic motion
c) periodic but not simple harmonic motion
The motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is
a) simple harmonic motion
b) non-periodic motion
c) periodic motion
d) periodic but not SHM
The correct answers are
a) simple harmonic motion
b) non-periodic motion
The displacement versus time curve for a particle executing SHM is shown in the figure. Choose the correct statements.
The correct answers are
b) phase of the oscillator is the same at t = 2 s and t = 6 s
d) phase of the oscillator is the same at t = 1 s and t = 5 s
Which of the following statements is/are true for a simple harmonic oscillator?
The correct answers are
a) force acting is directly proportional to the displacement from the mean position and opposite to it
b) motion is periodic
d) the velocity is periodic
The displacement time graph of a particle executing SHM is shown in the figure. Which of the following statement is/are true?
The correct answers are
a) the force is zero at t = 3T/4
b) the acceleration is maximum at t = 4T/4
c) the velocity is maximum at t = T/4
A body is performing SHM. Then its
a) average total energy per cycle is equal to its maximum kinetic energy
b) average kinetic energy per cycle is equal to half of its maximum kinetic energy
c) mean velocity over a complete cycle is equal to 2/π times of its maximum velocity
d) root mean square velocity is 1/√2 times of its maximum velocity
The correct answers are
a) average total energy per cycle is equal to its maximum kinetic energy
b) average kinetic energy per cycle is equal to half of its maximum kinetic energy
d) root mean square velocity is 1/√2 times of its maximum velocity
A particle is in linear simple harmonic motion between two points A and B, 10 cm apart. Taken the direction from A to B as the +ve direction, choose the correct statements.
The correct answers are
a) the sign of velocity, acceleration, and force on the particle when it is 3 km away from A going towards B are positive
c) the sign of velocity, acceleration, and force on the particle when it is 4 cm away from B going towards A are negative
d) the sign of acceleration and force on the particle when it is at point B is negative
Very Short AnswersDisplacement versus time curve for a particle executing SHM is shown. Identify the points marked at which
i) velocity of the oscillator is zero
ii) speed of the oscillator is maximum
i) When the points A, C, E, and G lie at their extreme positions, the velocity of the oscillator is zero.
ii) When the points B, D, F, and H lie at their mean positions, the speed of the oscillator is maximum.
Two identical springs of spring constant K are attached to a block of mass m and to fixed supports, as shown in the figure. When the mass is displaced from the equilibrium position by a distance x towards the right, find the restoring force.
Given,
F1 = -kx for the left spring
F2 = -kx for the right spring
Restoring force, F = F1 + F2 = -2kx
Therefore, when the spring is towards left, F = 2kx