Find the time for one complete vibration. Find the force constant of the spring.

Question

Find the time for one complete vibration.

Find the force constant of the spring.

Find the maximum speed of the mass.

Find the maximum magnitude of force on the mass.

I got the answers of the questions up there but I need help with the answers below.

A 1.10 kg mass on a spring has displacement as a function of time given by the equation xleft( t right) = left( {7.40;{rm{ cm}}} right),cos:left[ {left( {4.16;{rm{ rad/s}} } right)t - 2.42; {rm rad}} right]. Find the time for one complete vibration. Find the force constant of the spring. Find the maximum speed of the mass. Find the maximum magnitude of force on the mass. I got the answers of the questions up there but I need help with the answers below. -Find the position of the mass at t = 1.00;{rm{ s}}; -Find the speed of the mass at t = 1.00;{rm{ s}};

Explanation / Answer

at t=1s position, x(0)=7.4cos(4.16*1-2.42) =-1.25cm velocity,V(t)=7.4*4.16*(-sin(4.16t-2.42)) V(0)=7.4*4.16*(-sin(1.74)=30.34cm/s acceleration,=7.4*4.16^2*(-cos(4.16t-2.42)) =7.4*4.16^2*(-cos1.74) =21.56cm/s^2 magnitude of force=ma=1.1*0.2156 =0.237N

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