Question

The function

*x* = (4.8 m) cos[(3*π*rad/s)t + *π*/6
rad]

gives the simple harmonic motion of a body. At *t* = 5.6 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?

Answer #1

**compare the given equation with**

**x = A*cos(w*t + phi)**

**A = 4.8 m
w = 3*pi rad/s
phi = pi/6 rad**

**at t = 5.6 s
a)**

**x = 4.8*cos(3*pi*5.6 + pi/6)**

**= -4.77 m**

**b) v = dx/dt**

**= A*w*(-sin(w*t + phi))**

**at t = 5.6 s**

**v = -4.8*3*pi*sin(3*pi*5.6 + pi/6)**

**= -4.73 m/s**

**c) a = dv/dt**

**= -A*w^2*cos(w*t + phi)**

**= -A*w^2*x**

**= -4.8*(3*pi)^2*(-4.77)**

**= 2034 m/s^2**

**d) phase of the motion = w*t + phi**

**= 3*pi*5.6 + pi/6
= 53.3 rad**

**e) frequency, f = w/(2*pi)**

**= 3*pi/(2*pi)**

**= 1.50 Hz**

**f) T = 1/f**

**= 1/1.5**

**= 0.67 s**

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1)x = (9.2 m) cos[(5πrad/s)t + π/4
rad]
gives the simple harmonic motion of a body. At t = 2.1 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?
2) An oscillating block-spring system takes 0.746 s to begin
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(b) the frequency in hertz, and
(c) the angular frequency in radians per
second.

please double check the answers of Question 1 C and Question 2 D
i got the rest of the answers.
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