Please help me describe the motions with equations, THANKS! A mass m is attached

Question

Please help me describe the motions with equations, THANKS!

A mass m is attached to two springs that have relaxed lengths of zero. The other ends of the springs are fixed at two points (see Fig. 1). The two spring constants are equal. The mass sits at its equilibrium position and is then given a kick in an arbitrary direction. Describe the resulting motion. (ignore gravity) A mass m is attached to n springs that have relaxed lengths of zero. The other ends of the springs are fixed at various points in space (see Fig. 2). The spring constants are k1, k2,...,kn. The mass sits at its equilibrium position and is then given a kick in an arbitrary direction. Describe the resulting motion. (ignore gravity)

Explanation / Answer

a) F = -kx - kx = -2kx

ma = -2kx

m x'' + 2 kx = 0

divide ny m

x'' + 2 k/m x = 0 ( eqn of motion , w^2 = 2k/m)

b) Similarly as above

x" + n k/m x = 0 ( eqn of motion , w^2 = nk/m)

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