35 tion of the particle when t= 0.500 s.from the origin to x = 5.00 cm and released from rest at / = 0.ity and the maximum acceleration of the particle? (f) Deter-the amplitude of the motion? (e) What are the maximum veloc-motion? (c) What is the total energy of the system? (d) What ismine the displacement x of the particle from the equilibriumUnless otherwise noted, all content on this page is © Cengage Learning.33. Given that x = A cos (wi) is a sinusoidal function of time, showangular frequency w, the frequency, and the period of the(a) What is the force constant of the spring? (b) What are theattached to the free end of the spring. The particle is displacedand ispartic41. The sipositiv(a) arthe wa0.500 s. (g) Determine the velocity and accelera-positionchat v (velocity) and a (acceleration) are also sinusoidal func-tions of time. Hint: Use Equations 13.6 and 13.2.42. An13.5 Motion of a Pendulummo(a)(d)(f)84. VA man enters a tall tower, needing to know its height. Henotes that a long pendulum extends from the ceiling almostto the floor and that its period is 15.5 s. (a) How tall is thetower? (b) If this pendulum is taken to the Moon, where thefree-fall acceleration is 1.67 m/s², what is the period there?35. A simple pendulum has a length of 52.0 cm and makes 82.0 com-plete oscillations in 2.00 min. Find (a) the period of the pendu-lum and (b) the value of gat the location of the pendulum.36. A “seconds" pendulum is one that moves through its equilib- boorium position once each second. (The period of the pendulum leois 2.000 s.) The length of a seconds pendulum is 0.992 7 mat Tokyo and 0.994 2 m at Cambridge, England. What is theratio of the free-fall accelerations at these two locations?

Given in time t=2.0min the pendulum completed n=82 oscillations. Length of the pendulum is L=52.0cm=0.52m We know the time period is defined as time needed to complete one full oscillation. We know 1min=60sec. Therefore the time period of the pendulum is This is the time period. Now we know the time period of a pendulum having length L in gravity g is given by Putting the values we get This is the value of g.

Answered: 35. A simple pendulum has a length of…

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35. A simple pendulum has a length of 52.0 cm and makes 82.0 com- plete oscillations in 2.00 min. Find (a) the period of the pendu- lum and (b) the value of gat the location of the pendulum.