Answer:
Amplitude= -0.03087m
Explanation
Note that the total momentum before collision is equal to the momentum after collision.also
Energy Before Collision = Energy After Collision
the parameters are as follows
m1=6kg
m2=2kg
T=20ms=.02s
v1=6m/s
t=5ms=.005
x = (1.0 cm) cos (ωt + π/2)
There are some other equation tat could be useful
ω=2πf
ω=[tex]\sqrt{k/m^2}[/tex]
f=1/T
kinetic energy is Ek=0.5mv^2
Energy in spring=Es=0.5kx^2
Lets compute energy before collision
kinetic energy of block 1 =0.5m1v1^2
energy of block 2 which is a spring is =0.5kx^2
to find k, recall that ω=[tex]\sqrt{k/m^2}[/tex]
We can find ω=2πf ,
f=1/T ,f=1/0.02=50HZ
2*PI*50
ω=100πrad/s
ω=[tex]\sqrt{k/m^2}[/tex]
ω^2m2=k ........find the square root of both sides
k=197317
to find x, remember the position of the spring
x = (1.0 cm) cos (ωt + π/2)
ω=100πrad, t=0.005s
x = (0.01) cos (100πrad*0.005s + π/2)=
-0.01m
energy of block 1=0.5*4*6=72J
ENERGY OF SPRING=0.5*2*(100π)^2 -0.01^2=9.86J
energy before collision will be=e1+e2= 72+9.86
81.86J
energy after collision will be Eafter=0.5kx^2
0.5kx^2=0.5m*ω^2 *x^2
m=m1+m2= 6kg
ω=[tex]\sqrt{k/m^2}[/tex]=(197317/6)^0.5
181.3rad/s
Energy Before Collision = Energy After Collision
81.86J=(0.5)*(6)*181.3rad/s^2(x^2)
x=0.0288m
Amplitude can now be found since we have gotten all the parameters
x=A cos (ωt + π/2)
0.0288m=A cos (181.3rad/s*(0.005)+ π/2)
A= -0.03087m
