Homework Answers
The mass here is undergoing Simple Harmonic Motion(SHM),
Time taken from one peak to another peak is nothing but Time period which is given by the formula
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During free vibration of a spring-mass system in one direction, the mass m undergoes a displacement...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
A mass of m kilograams (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixced to the ground. The mass moves vertic...
A mass of m kilograams (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixced to the ground. The mass moves vertically up and down, acted on by gravity, the restoring force T of the spring and the damping force R due to friction: see the diagram below The gravitational force is mg dowswards, where g- 9.8m is acceleration due to gravity, measured...
An ideal mass m is sitting on a plane,attached to a rigid surface via a spring. The spring consta...
An ideal mass m is sitting on a plane,attached to a rigid surface via a spring. The spring constant is k, damping coefficient is c, and r(t) is the displacement of the mass with respect to the equilibrium position at time t. damper r 丑 spring Whent 0, we start to measure this of mass v(0)0 system and displacement o )1, velocity a) How many times will the mass pass through the equilibrium position in one b) Please find the...
Consider a single degree of freedom (SDOF) with mass-spring-damper system
Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics: Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f0 = 5 N; forcing frequency, ωt = 30 rad/s. (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped. (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
A spring-mass system has a
spring constant of 3 N/m. A mass of 2 kg is attached to the spring,
and the motion takes place in a viscous fluid that offers a
resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
A block-spring system undergoes simple harmonic motion with an amplitude A. 3.1 If the mass is...
A block-spring system undergoes simple harmonic motion with an amplitude A. 3.1 If the mass is doubled but the amplitude remains unchanged, how will this affect the total energy of the system? 3.2 Can the displacement and the acceleration of the mass be In the same direction? Explain.
Question (b) Ans : root(7/2) , 16/((5)^(1/2)) 9. Consider a mass-spring system as shown in the...
Question (b)
Ans : root(7/2) , 16/((5)^(1/2))
9. Consider a mass-spring system as shown in the figure with a body of mass m, a spring and a dashpot. Let k, c and r(t) be the spring constant, the damping constant and driving force, respectively Let y(t) be the displacementMass of the body from the equilibrium with downward direction as positive. b) [7pts] Let m=1, c=1, k=4, and r(t) 8cosut. Determine w such that you get the steady-state vibration of maximum...
> DOF Free Vibration An o rweligible mass and length move in the vertical plane by...
> DOF Free Vibration An o rweligible mass and length move in the vertical plane by spring and massen hux - 100 min the mass and length is pivoted at the middle point and 18 and masseo, shown. I - 123 m h Bite the Equations of Motion in Matrix Form ind the natural frequencies Find the mode shapes
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
A mass of m kilograams (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixced to the ground. The mass moves vertically up and down, acted on by gravity, the restoring force T of the spring and the damping force R due to friction: see the diagram below The gravitational force is mg dowswards, where g- 9.8m is acceleration due to gravity, measured...
An ideal mass m is sitting on a plane,attached to a rigid surface via a spring. The spring constant is k, damping coefficient is c, and r(t) is the displacement of the mass with respect to the equilibrium position at time t. damper r 丑 spring Whent 0, we start to measure this of mass v(0)0 system and displacement o )1, velocity a) How many times will the mass pass through the equilibrium position in one b) Please find the...
A spring-mass system has a
spring constant of 3 N/m. A mass of 2 kg is attached to the spring,
and the motion takes place in a viscous fluid that offers a
resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
Question (b)
Ans : root(7/2) , 16/((5)^(1/2))
9. Consider a mass-spring system as shown in the figure with a body of mass m, a spring and a dashpot. Let k, c and r(t) be the spring constant, the damping constant and driving force, respectively Let y(t) be the displacementMass of the body from the equilibrium with downward direction as positive. b) [7pts] Let m=1, c=1, k=4, and r(t) 8cosut. Determine w such that you get the steady-state vibration of maximum...
> DOF Free Vibration An o rweligible mass and length move in the vertical plane by spring and massen hux - 100 min the mass and length is pivoted at the middle point and 18 and masseo, shown. I - 123 m h Bite the Equations of Motion in Matrix Form ind the natural frequencies Find the mode shapes
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
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