665 6.7 Harmonic Motion 11. Particle Movement Write the equation and then determine the amplitude, period, and frequency of the simple harmonic motion of a particle moving uniformly around a circle of radius 2 units, with the given angular speed. (a) 2 radians per sec (b) 4 radians per sec 12. Spring Motion The height attained by a weight attached to a spring set in motion is s1t2 = -4 cos 8pt inches after t seconds. (a) Find the maximum height that the weight rises above the equilibrium position of s1t2 = 0. (b) When does the weight first reach its maximum height if t Ú 0? (c) What are the frequency and the period? 13. Pendulum Motion What are the period P and frequency T of oscillation of a pendulum of length 1 2 ft? AHint:P = 2p3 L 32, where L is the length of the pendulum in feet and the period P is in seconds.B 14. Pendulum Motion In Exercise 13, how long should the pendulum be to have a period of 1 sec? 15. Spring Motion The formula for the up and down motion of a weight on a spring is given by s1t2 = a sinAk m t. If the spring constant k is 4, what mass m must be used to produce a period of 1 sec? 16. Spring Motion (See Exercise 15.) A spring with spring constant k = 2 and a 1-unit mass m attached to it is stretched and then allowed to come to rest. (a) If the spring is stretched 1 2 ft and released, what are the amplitude, period, and frequency of the resulting oscillatory motion? (b) What is the equation of the motion? 17. Spring Motion The position of a weight attached to a spring is s1t2 = -5 cos 4pt inches after t seconds. (a) Find the maximum height that the weight rises above the equilibrium position of s1t2 = 0. (b) What are the frequency and period? (c) When does the weight first reach its maximum height? (d) Calculate and interpret s11.32 to the nearest tenth. 18. Spring Motion The position of a weight attached to a spring is s1t2 = -4 cos 10t inches after t seconds. (a) Find the maximum height that the weight rises above the equilibrium position of s1t2 = 0. (b) What are the frequency and period? (c) When does the weight first reach its maximum height? (d) Calculate and interpret s11.4662. 19. Spring Motion A weight attached to a spring is pulled down 3 in. below the equilibrium position. (a) Assuming that the frequency is 6 p cycles per sec, determine a model that gives the position of the weight at time t seconds. (b) What is the period? m
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