(a) The position of a mass in a spring-mass system
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(a) The position of a mass in a spring-mass system is given as x(t) = 2cos4t. Find the period of
oscillations and initial conditions.
(b) Consider a vertical spring mass-damper-system with mass m = 2 kg, damping coefficient c = 5 N.s/m
and stiffness k = 10 N/m. An external force f(t) = sin3t N is applied to the mass.
(i) Find the static equilibrium position as measured from the un-stretched length of the spring
(ii) Write the equation of motion.
(iii) Find the natural and damped frequencies.
(iv) In steady state, find the time delay in seconds between the mass position and f(t).
(v) Find the steady state maximum acceleration.
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