Single degree of freedom vibration problems with forcing functions

Need help with this Undergraduate problem where two dampers are in series.

For a vertical spring/damper system with mass (M) and a harmonic forcing function, Fmax Cos [omega x t] , two dampers are in series with coefficients, C1 and C2, and a single spring with constant, k.

Determine the amplitude of the steady-state displacement.

For this two degree fo freedom model, how do I find the matrix equation of motion?
How do I find the value of the modal ratios if m1=m2=m, k1=k and k2=3k?
If a force of 25sin3t is applied to m2, how do I find the value of the response if m1=m2=1 slug, k1=10lb/ft and k2=30lb/ft?

A mass of 0.3 kg is suspended from a spring of stiffness 200 N m-1. If
the mass is displaced by 10 mm from its equilibrium position and
released, for the resulting vibration, calculate:
(a) (i) the frequency of vibration.
(ii) the maximum velocity of the mass during the vibration.
(iii) the maximum acceleration of the

1) For the two degree of freedom structure shown:
i) what is the matrix equation of motion?. Assume that m1 and m2 oscillate harmonically with the same frequency but with different amplitudes X1 and X2 of x1(t) and x2(t).
ii) what are the values of the amplitude ratios r1 and r2
if m1 = m2 = m, k1 = k, and k2 =3k?
See a

Use the calculator provided to solve the following problems.
- Consider a t distribution with 29 degrees of freedom. Compute P(t<=1.19)nd your answer to at least three decimal places.
- Consider a t distribution with 22 degrees of freedom. Find the value of c such that
P (-c < t < c)=0.95. Round your answer to at least

A 0.50-kg mass is attached to a spring with a spring constant of 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What is the amplitude of vibration?

Plot the response x of the 20kg body ( see figure 1, attached) over the time interval 0/1 second. Determine the maximum and minimum values of x and their respective times. The initial conditions are X0=0 and dx/dt=2m/s.

You have a mass-spring system, a unit impulse is applied to this system (at equilibrium,at rest) and the response is recorded and determined to be
(10e^-0.1t)- (10e^-0.2t)
In general terms what does the form of the impulse response function tell you about the system?

Use the t-distribution table to find the critical value(s) for the indicated alternative hypothesis, level of significance ?, and sample sizes n? and n?. Assume that the samples are independent, normal, and random.
H?: µ? < µ?, ? = 0.05, n? = 14, n? = 13
(a) Find the critical value(s) assuming the population variances