Simple harmonic motion derivative of position function

[jdawg]

Homework Statement

The function
x = (7.4 m) cos[(5πrad/s)t + π/5 rad]
gives the simple harmonic motion of a body. At t = 6.2 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?

Homework Equations

The Attempt at a Solution

Hi! I understand that you're supposed to plug in your t into the position function, and then take the derivative and continue plugging in. I think I'm messing up the math somehow because I keep getting the wrong answer...

(7.4)cos(98.0177)= -0.1395

 

[jdawg]

So I went ahead and tried to derive the position function, and I feel like I did it correctly. However, I'm still getting incorrect answers when plugging in my t value.

v(t)= -7.4sin(5$\pi$t+$\frac{\pi}{5}$)*5$\pi$
v(6.2)= -115 m/s

a(t)= -7.4cos(5$\pi$t+$\frac{\pi}{5}$)*5$\pi$*5$\pi$
a(6.2)= -255 m/s²

 

[STEMucator]

For a) I'm getting -5.987 m.

For b) your derivative looks fine to me. I'm getting 68.324 m/s for the velocity though.

c) I'm getting -1825.880 m/s^2.

Is your calculator in degree mode perhaps?

 

[jdawg]

For a) I'm getting -5.987 m.

For b) your derivative looks fine to me. I'm getting 68.324 m/s for the velocity though.

c) I'm getting -1825.880 m/s^2.

Is your calculator in degree mode perhaps?

Haha ohh, thanks so much! That was the problem :)

 

[HalfLostAndSearching]

m

To find velocity:
v= -7.4sin(98.0177)(5πrad/s) = -36.79 m/s

To find acceleration:
a = -7.4cos(98.0177)(5πrad/s)^2 = 183.95 m/s^2

To find phase:
The phase of the motion can be found by taking the inverse cosine of the ratio of the displacement and amplitude. In this case, it would be arccos(-0.1395/7.4) = 1.878 rad.

To find frequency:
The frequency of the motion can be found by taking the coefficient of t in the position function, which is 5πrad/s.

To find period:
The period of the motion can be found by taking the inverse of the frequency, which is 1/(5πrad/s) = 0.0637 s.