Homework 01\ Solve the following:\ Figure (1) shows a block of mass

m

that can slide without friction along a horizontal surface. The mass is attached to a spring with spring constant

k

which is attached to a wall on the other end.\ a) If the amplitude of oscillation of the mass is given by

A

, derive a mathematival expression that describe that velocity at any location along the path

v(x)

.\ b) Calculate the velocity of the oscillating mass at

x=3mm

if the mass is

m=1kg

and amplitude of oscillation of the mass is

25mm

.\ c) What will be the velocity of the oscillating mass at

x=3mm

if the amplitude of oscillation is

A=

75mm

.\ d) What is the phase shift will be (

\\\\Phi

value) if the mass spring system has the following initial conditions:\

x=A

when

t=0

.\

x=0

, when

t=0

.