A mass of 100 kg stretches an undamped spring by 10 cm. Assume that g = 10 m/s 2

Question

A mass of 100 kg stretches an undamped spring by 10 cm. Assume that g = 10 m/s2.
Include the correct units in all your answers below.
(a) Find the spring constant k and its correct unit.
(b) Set up the second order differential equation which governs the motion of the
spring-mass system, choosing the x-axis to be oriented downwards. Find the general solution of this equation.
(c) Find the particular solution of the equation if the mass is released 50 cm below the equilibrium position from rest.
(d) What is the first positive time at which the mass returns to the equilibrium position?

Explanation / Answer

dx = 10 cm = 0.1 m

a) spring constant K = F/dx = m*g/dx = (100*9.8)/0.1 = 9800 N/m <-----answer

b) d^2x/dt^2 + w^2x = 0 <-----answer

x = xo*sin(wt + phi) <-----answer

c) x = 50*sin(wt+phi) <-----answer

d) Time period of the spring = 2*pi*sqrt(m/k) = 2*pi*sqrt(100/9800) = 0.634 s

time taken t = TT/4 = 0.16 <-----answer

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