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HoldingOn

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A particle moves in SHM with acceleration given by x^(..)=-6x ms^2. When x=2, v=+-4.
a. Find the period
b. The amplitude
c. Find the maximum velocity and acceleration

Thanks in advance
 

fan96

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From the reference sheet we have , where the period is given by

.

Clearly , so

.

Now,



Substituting in the initial conditions gives .



The maximum value of occurs when (). Therefore the maximum velocity is .

Note that since must be non-negative, we have a restriction on , which is



Therefore the amplitude is .

Finally, going back to the first equation:



The maximum acceleration occurs for the lowest possible value of , which is . This gives .
 

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