Question

In: Advanced Math

1. A mass weighting 8 pounds is suspended from a spring whose spring constant is 9...

1. A mass weighting 8 pounds is suspended from a spring whose spring constant is 9 lb/ft. There are no damping or
external forces. The mass is then released from an initial position of 5 feet above the equilibrium position with an
initial downward velocity of 30 ft/sec. (Note: Use g = 32 ft/sec!)
a) Write down an initial value problem modeling this situation.
b) Find the equation of motion.
c) What are the amplitude, period, and frequency of the simple harmonic motion?
d) At what time does the mass pass through the equilibrium position heading upward for the first time, if ever?
Explain your answer.

Solutions

Expert Solution


Related Solutions

A mass of 2 kg is suspended from a spring with known spring constant of 10N/m...
A mass of 2 kg is suspended from a spring with known spring constant of 10N/m and allowed to come to rest. it is then set in motion by giving it an initial velocity of 150 cm/sec. Find an expression for the motion of the mass, assuming no air resistance.
A mass suspended at the end of a light Spring and spring constant K is set...
A mass suspended at the end of a light Spring and spring constant K is set into vertical motion use lagrange's equation to find the equation of motion of the mass
A body whose mass is 1.82 kg is suspended from a spring of negligible mass , and is found to stretch the spring 3.12 cm.
A body whose mass is 1.82 kg is suspended from a spring of negligible mass , and is found to stretch the spring 3.12 cm. (i) What is the force constant of the spring? (ii) What is the period of oscillation of the body, if pulled down and released? (iii) What would be the period of a body weighing 3.63 kg, hanging from the same spring?
A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from...
A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. Find the equation of motion (solve the IVP) if the mass is driven by an external force equal to f(t) = 5 cos(2t). Graph the solution. What part of 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 mass m = 1 kg is suspended from a spring that is stretched 1 cm...
A mass m = 1 kg is suspended from a spring that is stretched 1 cm under the influence of the weight of this mass. Now a periodic force is applied external of F (t) = 200 cos (vt) on the mass, which was initially in static balance. Disregarding all friction, get a relationship for position of the mass as a function of time, x (t). Also determine the value of ω which will cause resonance to occur
The displacement of a block of mass 1.280 kg attached to a spring whose spring constant...
The displacement of a block of mass 1.280 kg attached to a spring whose spring constant is 50 N/m is given by x = A cos ωt, where A = 12 cm. In the first complete cycle, find the values of x and t at which the kinetic energy is equal to one half the potential energy.
1) When a mass of 3 kilograms is attached to a spring whose constant is 48...
1) When a mass of 3 kilograms is attached to a spring whose constant is 48 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f(t) = 180e−4t cos(4t) is applied to the system. Find the equation of motion in the absence of damping. x(t) = 2) Solve the given initial-value problem. d^(2)x/dt^2 + 9x = 5 sin(3t), x(0) = 6,  x'(0) = 0 x(t) =
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 3 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 10 cos(3t). (Use g = 32 ft/s2 for the acceleration due to...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 5 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration due to...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT