Calculate Maximum Force Acting on 24 kg Mass

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To calculate the maximum force acting on a 24 kg mass described by the position function x(t) = 7sin(5t), the acceleration x'' must be determined. The relationship F = ma indicates that the force is the product of mass and acceleration. The acceleration is derived as x'' = -35sin(5t), with its maximum value occurring when sin(5t) equals 1, leading to a maximum acceleration of 35 m/s². Consequently, the maximum force is calculated as F = 24 kg * 35 m/s², resulting in a maximum force of 840 N. The error in the calculation stemmed from misidentifying the maximum value of the sine function in relation to time.
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The position of a mass m = 24 kg is given (in m) by x(t) = 7sin(5t). Calculate the magnitude of the maximum force acting on the mass.

All I know is that double prime equals acceleration, but I'm not even sure it that will help me solve the problem.

Anyone have any suggestions?
 
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Right...x'' is acceleration. And from that F = ma = mx''. All you have to do is find at what time(s) x'' is at its maximum value. Hint: The maximum value of sin t or cos t is 1.
 
I got x'' to equal -.053308sin(5t) then at maximum height t equals 54, but y doesn't equal 1.

What did I do wrong?
 

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