Question

In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 7.00 cos (4t + ) where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. 6.30 cm (b) At t = 0, find velocity of the piston. -9.11 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. -56.761 How do you find the acceleration a(t) of an object if you know the velocity as a function of time, v(t)? cm/s2 (d) Find the period and amplitude of the motion. 2.09 period Remember that 4 = w has units of radians per second. How do you determine the period from the angular frequency? s amplitude The amplitude is the maximum displacement of the object from the equilibrium point. How do you find this from the equation for x(t)? cm Need Help? Read It Watch It Talk to a Tutor

Answer 1

b)

v = dx / dt = - 28 sin( 4t + pi/7)

at t = 0

v = - 12.149 cm/s

=======

c)

a = dv/dt = - 28* 4* cos (4t + pi/7)

at t = 0

a = - 100.91 cm/s^2

=======

d)

w = 2 pi/ T

4 = 2 pi / T

T = 1.571 s

Amplitude = 7 cm

=====

Comment before rate in case any doubt, will reply for sure.. goodluck