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he function x = (5.6 m) cos[(3πrad/s)t + π/4 rad] gives the simple harmonic motion of...

he function x = (5.6 m) cos[(3πrad/s)t + π/4 rad] gives the simple harmonic motion of a body. At t = 9.7 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion?

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Answer #1

x = (5.6)cos(3pit +pi/4)

(a) t =9.7 s

x = 5.6 cos(3*pi*9.7 + pi/4)

x = -2.54 m

(b)v = dx/dt

v = -(5.6*3pi)sin(3pit+pi/4)

at t = 9.7 s

v = -(5.6*3pi)sin(3pi*9.7+pi/4)

v = 47.03 m/s

(c) a = dv/dt = -(5.6*3pi*3pi) cos(3pit +pi/4)

a = -(5.6*3pi*3pi) cos(3pi*9.7 +pi/4)

a = 225.83 m/s

(d) phase = 3pit +pi/4

= 3*pi*9.7 +pi/4= 92.2 rad

(e) w = 2pi*f = 3pi

f =1.5 Hz

(f) T = 1/f = 1/1.5

T = 0.67 s

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