.
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 = + .
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.