Solving a Simple Harmonic Motion Problem

[stacerho]

I can't figure out what the heck I need to do for this problem.


3) A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with the time according to the equation A=A sin (wt+ pi/3)

Where w=pi radians per second, t is in seconds, and a= 7.6m.
What is the phase of motion at t=2.6s? Answer in units of rad.

 

[Hootenanny]

Again, please show some working/effort.

 

[m2003]

I understand that solving problems related to simple harmonic motion involves understanding the properties and equations that govern this type of motion. In this case, we are given the equation A=A sin (wt+ pi/3) where A is the amplitude, w is the angular frequency, t is time, and pi/3 is the initial phase angle.

To solve this problem, we need to first identify the values given to us: w=pi radians per second, t=2.6s, and A=7.6m. We can then plug these values into the equation to find the displacement at t=2.6s.

A=7.6m
w=pi radians per second
t=2.6s

A=A sin (wt+ pi/3)
A=7.6m sin (pi*2.6+ pi/3)
A=7.6m sin (8.6pi/3)
A=7.6m sin (2.8667pi)
A=7.6m sin (2.8667*3.14)
A=7.6m sin (9)

Therefore, the displacement at t=2.6s is approximately 7.6m.

To find the phase of motion at t=2.6s, we need to find the angle in radians that corresponds to this displacement. This can be done by solving for the phase angle in the equation A=A sin (wt+ pi/3).

A=A sin (wt+ pi/3)
7.6m=7.6m sin (wt+ pi/3)
1=sin (wt+ pi/3)
wt+ pi/3= pi/2
wt= pi/2- pi/3
wt= pi/6

Therefore, the phase of motion at t=2.6s is pi/6 radians.

In summary, to solve this simple harmonic motion problem, we first identified the given values and then used the equation A=A sin (wt+ pi/3) to find the displacement and phase of motion at t=2.6s. By understanding the principles and equations of simple harmonic motion, we were able to successfully solve this problem.