Question #271612

The position of a SHO as a function of time is given by **x = 7.1cos 7πt + π **

** 3 6**

where **t** is in seconds and **x** is in centimetres. Find:

a) the period and frequency expressed as fractions

b) the velocity at **t = 2.5 **(to 2 sig. fig.)** **

Expert's answer

"x=7.1\\cos(7\\pi t+\\pi\/36)". So, we have

a) "T=2\\pi\/\\omega=2\\pi\/(7\\pi)=2\/7\\ (s)"

"f=1\/T=1\/(2\/7)=7\/2\\ (Hz)"

b) "v=dx\/dt=-1.56\\cdot\\sin(7\\pi t+\\pi\/36)"

"v(2.5)=-1.56\\cdot\\sin(7\\pi \\cdot2.5+\\pi\/36)=-1.6\\ (m\/s)"

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