Question

1. You are on a boat, which is bobbing up and down. The boat's vertical displacement y is given by y 1.2 cos(t). Find the amplitude, angular frequency, phase constant, frequency, and period of the motion. (b) Where is the boat at t 1 s? (c) Find the velocity and acceleration as functions of time t. (d) Find the initial values of the position, velocity, and acceleration of the boat. Ans: 1.2 m, 1/2 rad/s, T/6 rad, 0.0796 Hz, 12.6 s, 0.624 m, 1.04 m, -0.3 m, -0.260 m 2) An object oscillates with angular frequency w = 8.0 rad /s. At t 0, the object is at z 4 cm with an initial velocity-25 cm/s. (a) Find the amplitude and phase constant for the motion. (b) Write r as a function of time. Ans: 0.663 rad, 5.08 cm 3.) A 2-kg block is attached to a spring. The force constant of the spring is k 196 N/m. The agular frequency w, the frequency I, and the period T. (b) Write a as a function of block is held a distance 5 cm from the equilibrium position and is released at time. Ans: 9.90 rad/s, 1.58 Hz, 0.635 s 4.) A 3-kg object attached to a spring oscillates with an amplitude of 4 cm and a period of 2 s (a) What is the total energy? (b) What is the maximum speed of the object? (c) At what position z is the speed equal to half its maximum value? Ans: 0.0237 J,0.126 m/s, 3.46 cm 5.) A block attached to a spring oscillates vertically with a frequency of 4 Hz and an amplitud of 7 cm. A tiny bead is placed on top of the oscillating block just as it reaches its lowest int. Assume that the bead's mass is so small that its effect on the motion of the block is negligible. At what distance from the block's equilibrium position does the bead lose contact with the block? Ans: -1.55 cm 6. A 3-kg object stretches a spring 16 cm when it hangs vertically in equilibrium. The spring 5 cm and the object is released. Let U be the total potential is then stretched an additional energy of the spring-object-planet system. When the mass is at its maximum dis fron equilibrium find U spring is un-stretched. Ans: 0.230 J, -2.12 J 0 at the equilibrium position and (b) U-0when the with (a) U 7.) A uniform rod of mass AM and length L is free to rotate about a horizontal axis perpendicular the rod and through one end. (a) Find the period of oscillation for small angular displace- ments. (b) Find the period of oscillation if the rotation axis is a distance r from the center of mass

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Answer 1

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