Reference no: EM132396833

Questions -

Question 1 - The response of a system is given by: x(t) = 0.01 cos (60t) + 0.02 sin(60t) m.

Determine -

(a) The amplitude of motion.

(b) The period of motion.

(c) The frequency in Hz.

(d) The frequency in rad/s.

(e) The frequency in rpm.

(f) The phase angle (lead or lag in response).

(g) The response in the form of Equation: x(t) = Xsin (wt+Φ).

Question 2 - A machine of mass 50.0 kg is placed on an elastic foundation. A sinusoidal force of magnitude 50 N is applied to the machine. A frequency sweep reveals that the maximum steady-state amplitude of 1.7 mm occurs when the period of response is 0.52 s.

Determine:

a) The damping ratio of the foundation.

b) The equivalent stiffness.

Question 3 - Find the total response of a single degree of freedom system with m = 12kg, c = 22N-s/m, k = 4500N/m, x₀ = 0.03m and x^·₀ = 0 under the following conditions

(i) An external force F(t) = F₀cosωt acts on the system with F₀ = 110N and ω =12rad/s.

(ii) Free vibration with F(t) = 0.

Question 4 - Find, in terms of the stiffness k:

a) The natural frequencies and

b) The normal modes

of the spring-mass system shown in figure, which is constrained to move in the vertical direction only. Take n =2.