SOLUTION: A mass is suspended by a spring such that it hangs at rest 0.5 m above the ground. The mass is raised 40 cm and released at time t = 0 s,causing it to oscillate sinusoidally. If th

Algebra ->  Equations -> SOLUTION: A mass is suspended by a spring such that it hangs at rest 0.5 m above the ground. The mass is raised 40 cm and released at time t = 0 s,causing it to oscillate sinusoidally. If th      Log On


   

Question 1192745: A mass is suspended by a spring such that it hangs at rest 0.5 m above the ground. The mass is raised 40 cm and released at time t = 0 s,causing it to oscillate sinusoidally. If the mass returns to the high position every 1.2 s, determine the height of the mass above the ground at t = 0.7 s. Draw a sketch.
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
A mass is suspended by a spring such that it hangs at rest 0.5 m above the ground.
The mass is raised 40 cm and released at time t = 0 s,causing it to oscillate sinusoidally.
If the mass returns to the high position every 1.2 s, determine the height of the mass
above the ground at t = 0.7 s. Draw a sketch.
~~~~~~~~~~~~~~~~~~~~ 

It is about deriving the formula of harmonic oscillations.


    The mid-line of the sinusoid is y= 0.5 m.

    The amplitude is 0.4 m.

    The period is 1.2 seconds.

    The time shift is such that using cosine function is preferable.


So, I write

    y = 0.5 + 0.4%2Acos%28%282%2Api%2At%29%2F1.2%29.


Now, to calculate y at t = 0.7 seconds, substitute 0.7 instead ot t into the formula.


Keep in mind that values of "y" represent height of the mass above the ground.


Happy calculations (!)

Solved and explained.