A spring mass system with a natural frequency fn = 12 Hz is attached to a...

A spring mass system with a natural frequency fn = 12 Hz is attached to a vibration table. The table is set to vibrate at 16 Hz, 0.5 g maximum acceleration:

a. What is the amplitude of the table's motion in inches?

b. What is the magnification factor M of this undamped system?

c. What is the maximum displacement of the mass assuming no dampening?

d. What is the maximum acceleration of the mass assuming the packaging can be modeled as a viscous damper with a damping ratio of 0.2?

e. Is the motion of the mass in phase or out of phase with the motion of the table?

Expert Solution

genius_generous answered 1 year ago

A 190 g mass attached to a horizontal spring oscillates at a frequency of 4.90 Hz....

A 190 g mass attached to a horizontal spring oscillates at a frequency of 4.90 Hz. At t = 0s, the mass is at x = 5.60 cm and vx = -24.0 cm/s. Determine: The period The angular frequency The amplitude The phase constant

A 155 gg mass attached to a horizontal spring oscillates at a frequency of 3.70 Hz...

A 155 gg mass attached to a horizontal spring oscillates at a frequency of 3.70 Hz . At t =0s, the mass is at x= 6.40 cmcm and has v =− 45.0 cm/s . Determine: a)The maximum speed b)The maximum acceleration. c)The total energy. d)The position at t= 4.80 s

A 180 g mass attached to a horizontal spring oscillates at a frequency of 2.80 Hz....

A 180 g mass attached to a horizontal spring oscillates at a frequency of 2.80 Hz. At t = 0 s, the mass is at x=7.00 cm and has vx= -29.0 cm/s. Determine: The maximum speed, the maximum acceleration, the total energy, and the position at t = 4.40 s.

A 175 g mass attached to a horizontal spring oscillates at a frequency of 2.80 Hz....

A 175 g mass attached to a horizontal spring oscillates at a frequency of 2.80 Hz. At t =0s, the mass is at x= 7.00 cm and has vx =− 35.0 cm/s . Determine: The maximum speed. The maximum acceleration. The total energy. The position at t= 2.80 s . In the previous parts, the following was found: period = 0.357 s, angular frequency = 17.59 rad/s, amplitude = 7.277 cm, phase constant = 15.8679 degrees.

A 145 g mass attached to a horizontal spring oscillates at a frequency of 5.50 Hz....

A 145 g mass attached to a horizontal spring oscillates at a frequency of 5.50 Hz. At t = 0s, the mass is at x = 6.60 cm and has vx =− 35.0 cm/s. Determine: a) The maximum speed. b) The maximum acceleration. c) The total energy. d) The position at t = 3.20 s.

A car and the suspension system are a damped spring, mass system, with a natural frequency...

A car and the suspension system are a damped spring, mass system, with a natural frequency 2 Hz and a damping coefficient 0.2. The car drives at speed V over a road with sinusoidal roughness. The roughness wavelength is 20 m, with a amplitude of 50 cm. What speed does the maximum amplitude of vibration occur? What is the corresponding vibration amplitude? Please do not use an older solution.

When a 0.710 kg mass oscillates on an ideal spring, the frequency is 1.46 Hz ....

When a 0.710 kg mass oscillates on an ideal spring, the frequency is 1.46 Hz . A. What will the frequency be if 0.260 kg are added to the original mass? Try to solve this problem withoutfinding the force constant of the spring. B. What will the frequency be if 0.260 kg are subtracted from the original mass? Try to solve this problem without finding the force constant of the spring.

Drive the formula for the angular frequency of a mass attached to a horizontal spring exexuting...

Drive the formula for the angular frequency of a mass attached to a horizontal spring exexuting simple harmonic motion? Can anyone help me please?

spring-mass system has a spring constant of 3 Nm. A mass of 2 kg is attached...

spring-mass system has a spring constant of 3 Nm. 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 15cos(3t)−10sin(3t) N,determine the steady-state response in the form Rcos(ωt−δ). R= _________ ω=__________ δ=___________

A 10- kg mass is attached to a spring, stretching it 0.7 m from its natural...

A 10- kg mass is attached to a spring, stretching it 0.7 m from its natural length. The mass is started in motion from the equilibrium position with an initial velocity of 1 m/s in the downward direction. a. Find the equation of motion assuming no air resistance. b. When is the first time the mass goes through the equilibrium position after it was set in motion. c. Find the equation of motion assuming air resistance equal to -90x’(t) Newtons....

Question