Question

write a differential equation in terms of displacement s to model the motion of an undamped vertical spring with mass m. recall that the weight should equal the spring's restoring force.

s= displacement

t= time

m = mass

k = spring constant

using calculus show that s(t) = c1 cos is a solution to the differential equation.

s(t) C1 cos (sqrt ((k/rn) * t)) + c) sin (sqrt ( ( k/m) * t))

Show transcribed image text s(t) C1 cos (sqrt ((k/rn) * t)) + c) sin (sqrt ( ( k/m) * t))