In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 3.00 cos (5t + where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. We are given x as a function of time. For any x(t) you can determine the position at a particular time by putting that value into the function. cm (b) At t = 0, find velocity of the piston. How do you find the velocity v(t) of an object if you know the position as a function of time, x(t)? cm/s (c) At t = 0, find acceleration of the piston. cm/s2 (d) Find the period and amplitude of the motion. period amplitude cm

Write down the expression for period of a pendulum of length I and the gravitational field strength g. Please use Il * II for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate. For square root and power please use sqrt(A*B) and (A*B)^2. Please use the "Display response" button to check you entered the answer you expect. T=

A Ferris wheel has a radius of 25 m and its centre is 27 m above the ground. It rotates once every 40 seconds. Sandy gets on the Ferris wheel at its lowest point and then the wheel starts to rotate. a) Determine a sinusoidal equation that gives Sandy's height, h, above the ground as a function of the elapsed time, t, where h is in metres and t is in seconds. b) Determinc the first time, t (in scconds), when Sandy will be 35 m abovc the ground.

A 43 kg mass on the end of a spring with spring constant k = 1,470 oscillates with simple harmonic motion x = A cos (@t+@). Find the minimum time taken in seconds (to 3 decimal points) for the mass to travel from 0.81A to 0.54A.

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

Suppose the oscillatory motion of an object can be modeled using the equation s(t) = 3.1sin(8.5t) where time is measured in seconds and distance is measured in inches.  Find the number of cycles (oscillations) the object makes per second.  (Provide 4 decimal places.)