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**[SOLVED] Block- spring- bullet- harmonic motion...**

## Homework Statement

Your assignment is to make measurements of the muzzle velocity of a bullet. This measurig device consists of a 10kg block which rests on a horizontal surface of negligible mass and is attatched to a hooke's law spring. The other end of the springis fixed to the wall. The preliminary data sent to you shows a 9.72g bullet traveling horizontally and colliding with the block, and as a result of this impact the bullet -block combination compresses the spring 7.50cm. This bullet-block system then executes simple harmonic motion with a 0.775Hz frequency of oscillation.

a) Give the equation which describes the displacement of this system as a function of time

b) What is the value of the spring constant?

c) What is the max acceleration of the system

d) What is the value of the displacement at this acceleration?

e) What is the total energy of this system?

f) what is the muzzle velocity of the gun that fired the bullet?

## Homework Equations

v= omega/k

omega= 2pi*f

momentum equation for inelastic collision = > m1v1 + m2v2= (m1+ m2) vf

F= ma

F= -kx

## The Attempt at a Solution

**a) Give the equation which describes the displacement of this system as a function of time**

[tex]y(x,t)= A sin (\omega*t -kx)[/tex]

[tex]\omega= 2 \pi f= (0.775Hz)2\pi= 4.869 rad/s[/tex]

[tex]A= 7.50cm=> 0.0750m [/tex]

k=?

I need help Thanks.

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