A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at any time is described by x (7.0 cm)cos[2nt/(4.28 s)]. Determine the following. (a) period of the motion How may the period of oscillation be determined from an expression for the position of the oscillating mass at any time? s (b) frequency of the oscillations How is the frequency of oscillation related to the period of the oscillation? Hz (c) first time the mass is at the position x = 0 What fraction of a period does it take for the oscillating mass to go from the position of maximum positive displacement to the equilibrium position? s (d) first time the mass is at the site of maximum compression of the spring What fraction of a period does it take for the oscillating mass to go from the position of maximum positive displacement to the position of maximum negative displace ment? s

A pendulum has a period of 5.8 s.  If you were to transfer this pendulum to the surface of Mars (where g is 3.71 meters per second squared), what would the period (in seconds) be?

The relation between gravitational acceleration and period for a 1.0-m long 1 pendulum is , where 7 is the period in seconds and & represents the 2 ng %3D gravitational acceleration in metres per second squared (m/s2). a) The gravitational acceleration at the surface of Earth is about 9.8 m/s2. Find the period of a pendulum 1.0 m long. b) The gravitational acceleration on the moon is approximately of the gravitational 1 acceleration at the surface of Earth. Determine the period of a pendulum 1.0 m long on the moon. c) Captain Mirk and Mr. Spark land on one of seven planets in the Alpha Beta system. Mr. Spark sets up a pendulum 1.0 m long, and Captain Mirk measures its period to be 1.304 s. Use the table to help you determine which planet they are on. Planet Ulu 3.6 Proserpine Wunderland Rutabaga Ada Sirius-Lee Ikona 6.8 13.5 19.7 23.2 31.1 54.0

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