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Transcript
Oscillations Q 1 If the length of a simple pendulum is doubled what will be its new time period? Mark (1) View Answer Q 2 A pendulum clock is observed to give correct time at the equator. What will happen if the same pendulum clock is taken to the pole of the earth? Mark (1) View Answer Q 3 In which condition the motion of a simple pendulum is simple harmonic? Mark (1) View Answer Q 4 What is oscillatory motion? Mark (1) View Answer Q 5 What is periodic motion? Mark (1) View Answer Q 6 Is the damping force constant on a system executing SHM ? Mark (1) View Answer Q 7 Two simple pendulums of equal length cross each other at mean position. What is their phase difference? Mark (1) View Answer Q 8 A vertical U-tube of uniform cross section contains water upto a height of 0.5m. If water on one side is depressed a little and then released it performs SHM up and down. Calculate (a) time period and (b) angular frequency of the vibration. Marks (2) View Answer Q 9 If the period of oscillation of mass m suspended from a spring is 2s, find the period of mass 4m? Marks (2) View Answer Q 10 A mass m is vertically suspended from a spring of negligible mass. The system oscillates with a frequency v. Find the frequency of the system if a mass 4m is suspended from the same spring? Marks (2) View Answer Q 11 A body of mass m is suspended by a spring of spring constant k. When the body is depressed a little and released, find its frequency of oscillation? Marks (2) View Answer Q 12 Is rotation of earth about its axis is an example of SHM? Marks (2) View Answer Q 13 When displacement is one-fourth of the amplitude, find the fraction of the total energy which is kinetic? Marks (2) View Answer Q 14 The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 300 rev/min, what is its maximum speed? Marks (2) View Answer Q 15 When the displacement is one half of the amplitude, find the fraction of total energy which is potential? Marks (2) View Answer Q 16 The length of a simple pendulum executing SHM is increased by 21%. Find the percentage increase in the time period of the pendulum of increased length? Marks (2) View Answer Q 17 At what distance from the mean position is the kinetic energy in simple harmonic oscillaton equal to P.E ? Marks (3) View Answer Q 18 A simple pendulum of length l and having a bob of mass m is suspended in a car. The car is moving on a circular track of radius r with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position what will be its time period? Marks (3) View Answer Q 19 The total energy of a particle, executing SHM is independent of displacement. Explain. Marks (3) View Answer Q 20 A block of mass 5 kg executes simple harmonic motion under the restoring force of a spring. The amplitude and the time period of the motion are 0.1m and 3.14s respectively. Find the maximum force exerted by the spring on the block. Marks (3) View Answer Q 21 A block is resting on a piston which is moving vertically with simple harmonic motion of period 1.0s. At what amplitude of motion will the block and piston separate? What is the maximum velocity of the piston at this amplitude? Marks (3) View Answer Q 22 A simple harmonic motion is represented by y = 10Sin(20t+0.5). Write down its amplitude, angular frequency, frequency, time period and initial phase, if displacement is in metres and time in seconds? Marks (3) View Answer Q 23 The potential energy of a particle oscillating on x-axis is given by U=20+(x-2)2 where U is in joules and x is in metres. Total mechanical energy of the particle is 36 joules. (a) State whether the motion of the particle is simple harmonic or not? (b) Find the mean position. (c) Find the maximum kinetic energy of the particle. Marks (3) View Answer Q 24 A particle executes SHM with a time period of 2s and amplitude 5 cm. Find (a) Displacement (b) Velocity (c) Acceleration after 1/3 seconds. Marks (3) View Answer Q 25 Between the plates of the capacitor with potential difference V across its plates such that upper plate is negative. A ball with positive charge q and mass m is suspended by a thread of length l. If the electrostatic force acting on the ball is less than the gravitational force, what should be the period of the ball? Marks (3) View Answer Q 26 A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this spring, when displaced and released, oscillates with period of 0.60 seconds. What is the weight of the body? Marks (3) View Answer Q 27 A mass attached to a spring is free to oscillate, with angular frequency w, in a horizontal plane without friction or damping. It is pulled to a distance x0 and pushed towards the centre with a velocity v0 at a time t=0. Determine the amplitude of the resulting oscillations in terms of the parameters w, x0 and v0. Marks (5) View Answer Q 28 A uniform cylinder of mass m and radius r is attached to one end of the spring as shown in the fig on rough horizontal surface. If the cylinder is slightly displaced, then find the time period of the oscillation given that there is no slipping on the surface. Marks (5) View Answer Q 29 A particle is performing simple harmonic motion along x-axis with amplitude 4.0 cm and time period 1.2s. What is the minimum time taken by the particle to move from x =+2 cm to x =+4 cm and back again? Marks (5) View Answer