Physics: A0.38 kg mass is attached to a spring with a spring constant 106 n/m so that the mass is allowed to move on a horizontal frictionless surface. the mass is released from rest when the spring is compressed 0.109 m. find the maximum force on the mass. answer in units of n.

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A0.38 kg mass is attached to a spring with a spring - id0383614298, sarahbennett11p4yxlb

lizzy6629

08.01.2022

11.55 N

Explanation:

Given

mass m=0.38 kg

Spring constant k=106 N/m

initial compression x=0.109 m

mass will perform simple harmonic motion with general equation of motion given by

$x=A\sin \omega t$

where $x=Position\ of\ Mass$

$A=maximum\ Amplitude$

$\omega =Natural\ frequency\ of\ oscillation=\sqrt{\frac{k}{m}}$

$\omega =16.70 rad/s$

t=time

therefore acceleration is given by

$a=-A\omega ^2\sin \omega t$

$a_{max}=A\omega ^2$

initial compression is equivalent to max amplitude

thus A=0.109 m

$a_{max}=A\omega ^2=0.109\times (16.70)^2=30.405 m/s^2$

therefore Maximum Force $F=ma_{max}$

$F=0.38\times 30.405=11.55 N$

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