Theory of Machines Miscellaneous Moderate Questions and Answers

Theory of Machines Miscellaneous

Consider a single degree of freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is

A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10 cos(25t) N. At the steady state, the vibration amplitude of the mass is 40 mm. The damping coefficient (c, in Ns/m) of the dashpot is __________.

A single degree of freedom system has a mass of 2 kg, stiffness 8 N/m and viscous damping ratio 0.02. The dynamic magnification factor at an excitation frequency of 1.5 rad/s is ______

In a spring-mass system, the mass is m and the spring constant is k. The critical damping coefficient of the system is 0.1 kg/s. In another spring-mass system, the mass is 2m and the spring constant is 8k. The critical damping coefficient (in kg/s) of this system is ______.

Which of the following statements are TRUE for damped vibrations?
P. For a system having critical damping, the value of damping ratio is unity and system does not undergo a vibratory motion.
Q. Logarithmic decrement method is used to determine the amount of damping in a physical system.
R. In case of damping due to dry friction between moving surfaces resisting force of constant magnitude acts opposite to the relative motion.
S. For the case of viscous damping, drag force is directly proportional to the square of relative velocity.

X =	F	= 40 mm = 0.04
	√(k - mω²)² + (Cω)²

⇒ 0.04 =	10
	√(6250 - 10 × 25²)² + (C × 25)²

X =	F	= 40 mm = 0.04
	√(k - mω²)² + (Cω)²

⇒ 0.04 =	10
	√(6250 - 10 × 25²)² + (C × 25)²