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Raddy13
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- Determine the displacement response of a mass on a spring when subject to an acceleration impulse
I'm working on a project where we have a mass (50 kg) sitting on a spring (350 N/mm) and are subjecting it to a sudden impulse (20g) along the spring axis to simulate a shock. We have the profile of the acceleration defined as:
##a(t) = x''(t) = P\cdot \sin^2 (\pi \cdot t / T)##
Where P (peak acceleration) and T (pulse width) are known and fixed. I know the normal equation is:
##F(t) + m \cdot g = m \cdot x'' + b \cdot x' + k \cdot x##
The b term drops out since there is no damper in this system, but that's as far as I can make it and I'm about a decade removed from my differential equations class. Is it possible to determine the function x(t) response from the information I have?
##a(t) = x''(t) = P\cdot \sin^2 (\pi \cdot t / T)##
Where P (peak acceleration) and T (pulse width) are known and fixed. I know the normal equation is:
##F(t) + m \cdot g = m \cdot x'' + b \cdot x' + k \cdot x##
The b term drops out since there is no damper in this system, but that's as far as I can make it and I'm about a decade removed from my differential equations class. Is it possible to determine the function x(t) response from the information I have?
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