 #1
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 Homework Statement:

See the picture below. Initially, the system is at rest. Neglecting friction and mass of both spring and string,
a) what is initial acceleration of M? Assume initially the spring is at natural length ##L_1##
b) find the tension when the system moves for the first time
c) is total energy of system conserved?
d) after moving a distance ##x_o## towards the wall, M will stop. Find ##x_o##
e) find the equilibrium point of M, measured from initial position of M, when M oscillates
f) find the period of oscillation of system
 Relevant Equations:

∑F = m.a
Restoring force: F = k.x
ω = 2π / T
a) When the system is in motion for the first time, the force causing ##M## to move is contact force with ##m## so:
$$\Sigma F=M.a$$
$$N \sin \alpha=M.a$$
$$mg \cos \alpha \sin \alpha =M.a$$
$$a=\frac{mg \cos \alpha \sin \alpha}{M}$$
Is that correct?
b) Is acceleration of ##m## the same as ##M## when the system moves for the first time?
Thanks