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Two identical springs of spring constant k are attached to a block of mass m and to fixed supports as shown in Fig.. Show that when the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. Find the period of oscillations.

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A block whose mass is 1 kg is fastened to a spring. The spring has a spring constant of 50 N `m^(–1)`. The block is pulled to a distance x = 10 cm from its equilibrium position at x = 0 on a frictionless surface from rest at t = 0. Calculate the kinetic, potential and total energies of the block when it is 5 cm away from the mean

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A 5 kg collar is attached to a spring of spring constant 500 N `m^(–1)`. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by 10.0 cm and released. Calculate (a) the period of oscillation, (b) the maximum speed and (c) maximum acceleration of the

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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What is the length of a simple pendulum, which ticks seconds

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For the damped oscillator shown in Fig., the mass m of the block is 200 g, k = 90 N `m^(–1)` and the damping constant b is 40 g `s^(–1)`. Calculate (a) the period of oscillation, (b) time taken for its amplitude of vibrations to drop to half of its initial value, and (c) the time taken for its mechanical energy to drop to half its initial value.

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Which of the following examples represent periodic

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic

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Fig. depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion) ?

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Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion?

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is (a) at the end A, (b) at the end B, (c) at the mid-point of AB going towards A, (d) at 2 cm away from B going towards A, (e) at 3 cm away from A going towards B, and (f) at 4 cm away from B going towards

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion? (a) a = 0.7x (b) a = –200`x^2` (c) a = –10x (d) a =

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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The motion of a particle executing simple harmonic motion is described by the displacement function, x(t) = A cos (ωt + φ ). If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cm/s, what are its amplitude and initial phase angle ? The angular frequency of the particle is π `s^(–1)`. If instead of the cosine function, we choose the sine function to describe the SHM : x = B sin (ωt + α), what are the amplitude and initial phase of the particle with the above initial

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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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 balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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A spring having with a spring constant 1200 N `m^(–1)` is mounted on a horizontal table as shown in Fig. . A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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In Exercise , let us take the position of mass when the spring is unstreched as x = 0, and the direction from left to right as the positive direction of x-axis. Give x as a function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is (a) at the mean position, (b) at the maximum stretched position, and (c) at the maximum compressed position. In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial

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Figures correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure. Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial (t =0) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: (x is in cm and t is in s). (a) x = –2 sin (3t + π/3) (b) x = cos (π/6 – t) (c) x = 3 sin (2πt + π/4) (d) x = 2 cos

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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Figure (a) shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. A force F applied at the free end stretches the spring. Figure (b) shows the same spring with both ends free and attached to a mass m at either end. Each end of the spring in Fig. (b) is stretched by the same force F. (a) What is the maximum extension of the spring in the two cases ? (b) If the mass in Fig. (a) and the two masses in Fig. (b)

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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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 200 rad/min, what is its maximum speed

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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The acceleration due to gravity on the surface of moon is 1.7 m `s^(–2)`. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s ? (g on the surface of earth is 9.8 m

asked Mar 19, 2022 in 11th Physics by varun (6.7k points)

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