Problem 2. A projectile of mass m= 10 kg travelling with a velocity of 50m/s strikes and becomes embedded in a massless board supported by a spring of stiffness k-6.4x 104 N/m and a dashpot with damping coefficient, c. Im a) Determine the damping coefficient, c, for the fastest decay of the vibrations. b) For the value of c calculated above, determine the time required for the board to reach the maximum displacement. What is the value of the maximum displacement? (Hint: Velocity will be zero at the point of maximum displacement) c) [Bonus] What percentage of energy has been dissipated at the point of maximum displacement?

Q: The differential equation of motion The maximum displacement and the time of its occurrence.

A:

Q: The amplitude of vibration of a single degree of freedom spring-mass-damper system is observed to…

A: Given data: - The stiffness of the spring is K = 1516 N/m. The mass is M = 23.5 kg. The ratio of…

Q: A 10-lb weight is attached to a spring suspended from the ceiling. When the weight comes to rest,…

A: Given: W=10 lbx=1.5 inc=52 lbs/ft/secx0=3 in

Q: QUESTION 2 A vibrating system can be modeled with a mass weighs 20 kg and supported on springs and…

A: The objective of the question is to determine the displacement of a vibrating system after 1 second…

Q: A mass weighing 16 pounds stretches a spring 83 feet. The mass is initially released from rest from…

A:

Q: A force of 20 newton stretches a spring 1 meter. A 5 kg mass is attached to the spring, and the…

A: Solution: Given Data: F=20 N∆=1 mm=5 kgFD=10x.

Q: 3.33. The following data are given for a damped single degree of freedom mass-spring system: mass m…

A:

Q: (a) Determine the time (in seconds) at which the mass passes through the equilibrium position. (b)…

A:

Q: A box with a mass of 3m is on frictionless ground, attached to a wall (on the left-side of the box)…

A: Given: To find: Equations Stiffness and mass matrix Normal frequencies Motion of the masses

Q: A viscously damped single degree of freedom mass-spring system has a mass m of 2 kg, a spring…

A:

Q: vehicle weighing 5,000 lb is supported on four identical springs and four identical viscous dampers.…

A: For solution refer below images.

Q: A pump of mass 30 kg is supported on a support structure which has 4 springs arranged in parallel…

A:

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.