A bungee jumper undergoes simple harmonic motion with amplitude 3.5 m and frequency 0.135 Hz. Assume the bungee jumper follows the simple harmonic motion equation x=Acos(wt).
A. Determine the bungee jumper's velocity at 0.25 s
B. Determine the bungee jumper's velocity at 0.50 s
C. Determine the bungee jumper's velocity at 1.0 s
And this was the work shown:
displacement x=Acos(ωt)
A = 3.5 m
ω = 2π*f = 2π*0.135 rad/s = 0.848 rad/s
velocity v = dx/dt = -A*ω*sin(ωt)
v = -2.97*sin(0.848*t)
Note: calculator must be in RAD mode now!
A. v at t = 0.25 is -2.97*sin(0.212) = -0.625 m/s
B. v at t = 0.5 is -2.97*sin(0.424) = -1.22 m/s
C. v at t = 1.0s is -2.97*sin(0.848) = -2.23 m/s
***My only problem understanding this is where the -2.97 value comes from. How do I find this value using my calculator?*** Thanks
You have:
velocity v = dx/dt = -A*ω*sin(ωt)
so what is -A omega ?
A = 3.5
omega = 2 pi f = .848
so
- A omega = -2.968 or -2.97
To find the value of -2.97 using a calculator, you can follow these steps:
1. Enter the value of A (amplitude) into the calculator: 3.5.
2. Multiply it by the value of ω (angular frequency): 0.848.
3. Take the sine of the resulting value: sin(0.848*0.25), sin(0.848*0.50), sin(0.848*1.0) for parts A, B, and C respectively.
4. Once you have the sine value, multiply it by -A*ω: -3.5 * 0.848.
5. Calculate the final result: -3.5 * 0.848 * sin(0.848*0.25), -3.5 * 0.848 * sin(0.848*0.50), -3.5 * 0.848 * sin(0.848*1.0) for parts A, B, and C respectively.
By performing these calculations correctly, you should get the value of -2.97 to use in the velocity equation.