Question

In: Physics

A mass weighing 4 N is attached to a spring whose constant is 2 N/m. The...

A mass weighing 4 N is attached to a spring whose constant is 2 N/m. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 m above the equilibrium position with a downward velocity of 6 m/s. Determine the time at which the mass passes through the equilibrium position. (Use

g = 9.8 m/s2

for the acceleration due to gravity.)

s

Find the time after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position.

   s

What is the position of the mass at this instant?

   m

Solutions

Expert Solution

if u have any doubt u can ask me in comment box .....hope u like it ....


Related Solutions

A mass weighing 4 N is attached to a spring whose constant is 2 N/m. The...
A mass weighing 4 N is attached to a spring whose constant is 2 N/m. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 m above the equilibrium position with a downward velocity of 6 m/s. Determine the time at which the mass passes through the equilibrium position. (Use g = 9.8 m/s2 for the acceleration due to gravity.) 14​   s Find the time after the...
A mass of 2 kilogram is attached to a spring whose constant is 8 N/m, and...
A mass of 2 kilogram is attached to a spring whose constant is 8 N/m, and the entire system is then submerged in a liquid that imparts a damping force equal to 8 times the instantaneous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force f(t) = 2U(t−1)*e^(−2(t−1)) is applied. (a) Write f(t), the external force, as a piecewise function and sketch its graph. (b) Write the initial-value problem....
A vertical spring (ignore its mass), whose spring constant is 825 N/m , is attached to...
A vertical spring (ignore its mass), whose spring constant is 825 N/m , is attached to a table and is compressed down by 0.160 m. A)What upward speed can it give to a 0.360-kg ball when released? Express your answer to three significant figures and include the appropriate units. B) How high above its original position (spring compressed) will the ball fly? Express your answer to three significant figures and include the appropriate units.
a block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m...
a block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m . At t=0.2s, the displacement x=-0.3m, and the velocity v=-2.0m/s a) find the equation of displacement as a function of time b) sketch the displacement as a function of time for the first cycle starting t=0s
A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire...
A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. The mass is initially released from rest from a point 1 meter below the equilibrium position. 1. Show the Diagram, given and required only ( No need to solve, Thumbs up will only be given if 1 is followed.)
When a 5 kg mass is attached to a spring whose constant is 180 N/m, it...
When a 5 kg mass is attached to a spring whose constant is 180 N/m, it comes to rest in the equilibrium position. Starting at  t = 0, a force equal to  f (t)  =  20e−3t cos 6t  is applied to the system. In the absence of damping, (a) find the position of the mass when  t = π. (b) what is the amplitude of vibrations after a very long time
When a 6 kg mass is attached to a spring whose constant is 24 N/m, it...
When a 6 kg mass is attached to a spring whose constant is 24 N/m, it comes to rest in the equilibrium position. Starting at  t = 0, a force equal to  f (t)  =  42e−7t cos 4t  is applied to the system. In the absence of damping, (a) find the position of the mass when  t = π. (b) what is the amplitude of vibrations after a very long time?
When a 6 kg mass is attached to a spring whose constant is 294 N/m, it...
When a 6 kg mass is attached to a spring whose constant is 294 N/m, it comes to rest in the equilibrium position. Starting at  t = 0, a force equal to  f (t)  =  12e−4t cos 3t  is applied to the system. In the absence of damping, (a) find the position of the mass when  t = π. (b) what is the amplitude of vibrations after a very long time?
A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences...
A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences friction, which acts as a force opposite and proportional to the velocity, with magnitude 2 N for every m/s of velocity. The spring is stretched 1 meter and then released. (a) Find a formula for the position of the mass as a function of time. (b) How much time does it take the mass to complete one oscillation (to pass the equilibrium point, bounce...
a. A 0.5 kg mass attached to a linear spring, with spring constant 5 N/m and...
a. A 0.5 kg mass attached to a linear spring, with spring constant 5 N/m and damping constant 0.2 kg/s, is initially displaced 10 cm from equilibrium. (a) What is the natural frequency of oscillation? What is its period of oscillation? How long does it take for the amplitude to decrease to 10% of its starting value? How many oscillations have occurred in this time? What fraction of the initial energy remains after this time? b. Two traveling waves with...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT