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simple harmonic motion of spring and simple pendulum

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34. Block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of 7.0 rad/s. The drawing indicates the position of the block when the spring is unstrained. This position is labeled "x = 0 m." The drawing also shows a small bottle located 0.080 m to the right of this position. The block is pulled to the right, stretching the spring by 0.050 m, and is then thrown to the left. In order for the block to knock over the bottle, it must be thrown with a speed exceeding vo Ignoring the width of the block, find vo

The length of a simple pendulum is 0.79 m and the mass of the particle (the "bob") at the end of the cable is 0.24 kg. The pendulum is pulled away from its equilibrium position by an angle of 8.50° and released from rest. Assume that friction can be neglected and that the resulting oscillatory 'motion is simple harmonic motion. (a) What is the angular frequency of the motion? (b) Using the position of the bob at its lowest point as the reference level, determine the total mechanical energy of the pendulum as it swings back and forth. (c) What is the bob's speed as it passes through the lowest point of the swing

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The solution shows how to calculate parameters related to the simple harmonic motion of spring and simple pendulum in detail.

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Simple harmonic motion

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15. The displacement of a mass oscillating on a spring is given by x(t) = x_m * cos(wt + ph). If the initial displacement is zero and the initial velocity is in negative x direction, then the phase constant phi is:

16. Mass m, oscillating on the end of a spring with spring constant k, has amplitude A. Its maximum speed is

17. A 3 kg block, attached to a spring, executes simple harmonic motion according to x =2cos(50t) where x is in meters and t is in seconds. The spring constant of the spring is

18. If the length of a simple pendulum is doubled, its period will

19. A simple pendulum is suspended from a ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of the pendulum, in terms of its length L, g, and a is

20. Three physical pendulums, with mass m1, m2 = 2m1, and m3 = 3m1, have the same shape and size and are suspended at the same point. Rank them according to their periods, from shortest to longest.

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