Question

In: Mechanical Engineering

Determine the response of a mass-spring system when it is subjected to a half-sine pulse of...

Determine the response of a mass-spring system when it is subjected to a half-sine pulse of 250 dyne amplitude and 0.25? seconds duration. The mass is 20gm and the spring stiffness is 197.4 dynes/cm.

Solutions

Expert Solution

given data:

mass spring system subjected to half sine pulse having

time duration T=0.25 sec

mass of spring = 20gm

spring stiffness = 197.4 dynes/cm=197.4 gm/sec2

need to find out ?

1 dyne =gm.cm/sec2= Newton

natural frequency = m/s

frequency = m/sec

==3.14

= =4

=.785 which is less than 1.

as we know when the resonance frequency is less than natural frequency system is in oscillation conditaion


Related Solutions

Obtain the initial and residual shock spectra of a half sine pulse. What is the total...
Obtain the initial and residual shock spectra of a half sine pulse. What is the total shock spectrum?
A mass on a spring is subjected to an external force that looks like a triangular...
A mass on a spring is subjected to an external force that looks like a triangular wave: F(t) = 1+t from t=-1 to 0 F(t) = 1-t from t=0 to t=1 Periodicity = 2 The differential equation for the position of the mass (using Newton’s law) ends up being: x’’(t) + 2x’(t) + 101x(t) = F(t) 1. Find the generic homogeneous solution 2. Find the Fourier series of F(t) 3. Find the Fourier series of the particular solution (which is...
A mass m, stretches horizontally from a spring which has spring constant k, and is subjected...
A mass m, stretches horizontally from a spring which has spring constant k, and is subjected to a retarding force equal to bv, where v is the instantaneous velocity of the mass. A particle of mass 10 gm moves along the x axis under the influence of two forces. The first is a force (in g cm s-2) of attraction to the origin O which is 40 times the distance from O. The second is a damping force proportional to...
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant 9 lbin is suddenly set in motion at t=0 by an external force of 180cos(8t) lb, determine the position of the mass at any time. Assume that g=32 fts2. Solve for u in feet.
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant 9 lb/in is suddenly set in motion at t=0 by an external force of 99cos(20t) lb, determine the position of the mass at any time. Assume that g=32 ft/s2. Solve for u in feet.
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant 9 lbin is suddenly set in motion at t=0 by an external force of 33cos(20t) lb, determine the position of the mass at any time. Assume that g=32 fts2. Solve for u in feet. Enclose arguments of functions in parentheses. For example, sin(2x). u(t)=?
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant 9 lbin is suddenly set in motion at t=0 by an external force of 288cos(4t) lb, determine the position of the mass at any time. Assume that g=32 fts2. Solve for u in feet. Enclose arguments of functions in parentheses. For example, sin(2x).
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant 4 lbin is suddenly set in motion at t=0 by an external force of 63cos(12t) lb, determine the position of the mass at any time. Assume that g=32 fts2. Solve for u in feet.
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant...
If an undamped spring-mass system with a mass that weighs 24 lb and a spring constant 16 lbin is suddenly set in motion at t=0 by an external force of 432cos(8t) lb, determine the position of the mass at any time. Assume that g=32 fts2. Solve for u in feet. Enclose arguments of functions in parentheses. For example, sin(2x). u(t) = ?
1.) A mass-spring system consists of an object of mass 1 Kilogram connected to a spring...
1.) A mass-spring system consists of an object of mass 1 Kilogram connected to a spring with a stiffness of 9. The damping constant is 6. Derive the function (1) that determines the distance from the equilibrium point if the initial position is 3 meters from the equilibrium point and the initial speed is 3 meters per second. a.) What is the maximum distance from the equilibrium point? b.) Determine the general solution of the nonhomogeneous linear differential equation using...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT