In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the following expression, where x is in centimeters and t is in seconds. x = (5.00 cm) cos(5t + π/5) (a) at t = 0, find the position of the piston. webassign will check your answer for the correct number of significant figures. (b) what is its velocity? webassign will check your answer for the correct number of significant figures. (c) what is its acceleration? webassign will check your answer for the correct number of significant figures. (d) find the period and amplitude of the motion. period: webassign will check your answer for the correct number of significant figures. amplitude: webassign will check your answer for the correct number of significant figures.

(a) 4.06 cm

In a simple harmonic motion, the displacement is written as

(1)

where

A is the amplitude

is the angular frequency

is the phase

t is the time

The displacement of the piston in the problem is given by

(2)

By putting t=0 in the formula, we find the position of the piston at t=0:

(b) -14.69 cm/s

In a simple harmonic motion, the velocity is equal to the derivative of the displacement. Therefore:

(3)

Differentiating eq.(2), we find

And substituting t=0, we find the velocity at time t=0:

(c) -101.13 cm/s^2

In a simple harmonic motion, the acceleration is equal to the derivative of the velocity. Therefore:

Differentiating eq.(3), we find

And substituting t=0, we find the acceleration at time t=0:

(d) 5.00 cm, 1.26 s

By comparing eq.(1) and (2), we notice immediately that the amplitude is

A = 5.00 cm

For the period, we have to start from the relationship between angular frequency and period T:

Using and solving for T, we find

the simple machine has three main features. they are:

fulcrum is the center point or pivot point of the machine. effort is input force/ applied force. load is external force/ output.

the keisha 's machine labels are

x : load

y: fulcrum

z: lever

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.