Answer:
Equation of movement y(t)
[tex]y(t)=sin(10t-\pi/2)[/tex]
Amplitude: 1 inch
Period: 0.628 seconds
Step-by-step explanation:
If there is no friction, the amplitude will be the length it was streched from the equilibrium. In this case, this value is 1 inch
[tex]A=1\,inch[/tex]
The period depends on the mass and the spring constant.
The formula for the period is:
[tex]T=\frac{1}{f} =\frac{2/pi}{\omega} =2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{1}{100}}=2\pi*0.1=0.628\, s[/tex]
The model y(t) for the movement of the mass-spring system is
[tex]y(t)=A\cdot sin(\omega t +\phi)\\\\A=1\\\\\omega=\sqrt{k/m} =\sqrt{100/1}=10\\\\y(0)=Asin(\phi)=-A\\\\ \phi=arcsin(-1)=-1.571=-\pi/2\\\\\\y(t)=sin(10t-\pi/2)[/tex]
