8. 2/5 points | Previous Answers SerPOP5 12.P.014.m. My Notes Ask Your Teacher I

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8. 2/5 points | Previous Answers SerPOP5 12.P.014.m. My Notes Ask Your Teacher In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x- 4.00 cos (St+ where x is in centimeters and t is in seconds. (a) At t0, find the position of the piston. 3.464 (b) At t 0, find velocity of the piston. -12.5 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. 13.85 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. period Remember that 5 -o has units of radians per second. How do you determine the period from the angular amplitude4 3.14 frequency? s cm Need Help?adWateh It

Explanation / Answer

x = 4*cos (5t + pi/6)

Compare it with standard equation

x = A*cos (wt + phi)

w = 5 rad/sec

w = 2*pi/T

T = 2*pi/w = 2*pi/5 = 1.256 sec

A = Amplitude = 4

x = 4*cos (5t + pi/6)

V = dx/dt = d(4*cos (5t + pi/6))/dt

V = -4*5*siin (5t + pi/6)

At t = 0

V = -20*sin (5*0 + pi/6)

V = -10 cm/sec = -0.1 m/sec

a = dV/dt = d(-20*sin (5*t + pi/6))/dt

a = -100*cos (5t + pi/6)

Now at t = 0

a = -100*cos (5*0 + pi/6)

a = -86.60 cm/sec^2 = -0.866 m/sec^2

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