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A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance `x_0` and pushed towards the centre with a velocity `v_0` at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters ω, `x_0` and `v_0`. [Hint : Start with the equation x = a cos (ωt+θ) and note that the initial velocity is

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The displacement of a particle is represented by the equation `y = 3 cos (pi/ 4 - ωt)` . The motion of the particle

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The displacement of a particle is represented by the equation `y = sin^3 ωt` . The motion

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The relation between acceleration and displacement of four particles are given

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Motion of an oscillating liquid column in a U-tube

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A particle is acted simultaneously by mutually perpendicular simple hormonic motions `x = a cos ωt and y = a sin ωt` . The trajectory of motion of the particle will

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The displacement of a particle varies with time according to the relation `y = a sin ωt + b cos

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Four pendulums A, B, C and D are suspended from the same elastic support as shown in Fig. . A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse

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Fig. shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P

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The equation of motion of a particle is `x = a cos (α t )^ 2` . The motion

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A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2 . The period of oscillation

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When a mass m is connected individually to two springs S1 and S2 , the oscillation frequencies are ν 1 and ν 2 . If the same mass is attached to the two springs as shown in Fig. , the oscillation frequency would

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The rotation of earth about its axis

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Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point

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Displacement vs. time curve for a particle executing S.H.M. is shown in Fig. Choose the correct

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Which of the following statements is/are true for a simple harmonic

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The displacement time graph of a particle executing S.H.M. is shown in Fig. Which of the following statement is/are

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A body is performing S.H.M. Then

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A particle is in linear simple harmonic motion between two points A and B, 10 cm apart (Fig. ). Take the direction from A to B as the + ve direction and choose the correct

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Displacement versus time curve for a particle executing S.H.M. is shown in Fig. . Identify the points marked at which velocity of the oscillator is

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