Question

In an undamped mass-spring system, a metal ball of weight 20nt stretches the spring 40cm and the system is at rest.

(1) What will the frequency of the resulting harmonic oscillation be? (Use g=10m/sec^2)

(2) If this system is undamped and it is stretched by 20cm again and released with zero initial velocity, find the displacement y(t) of the ball at time t.

Answer #1

1. A 4 pound weight stretches a spring 6
inches. The mass is then released from an initial position of 4
feet below the equilibrium position with an initial upward velocity
of 24ft/s.
(a) What is the frequency of motion?
(b) Determine the first time the mass crosses the
equilibrium position. Round to 3 decimals places.
(c) Determine the first time the mass attains its
extreme displacement from the equilibrium position. Round to 3
decimal places.

Given the undamped spring/mass system
The weight is 8 N (Newtons)
The spring constant is 100 N/m
The length of the spring is 2 m.
At t=0, the spring is compressed 0.5 m, making the length 1.5
m.
Down is the positive direction
A)Determine the frequency of oscillations of the mass? (Include
units) maximum_displacement=
B)Determine the equilibrium position including units of the
spring with the mass attached (if the mass is not moving.)
Equalibrium_position=
C)What is the restoring force of...

A mass weighting 8 lbs stretches a spring 2 inches. The mass is
in a medium that exerts a viscous resistance of 3 lbs when the mass
has a velocity of 6 ft/sec.
Suppose the object is displaced an additional 7 inches and
released.
Find an equation for the object's displacement, u(t), in
feet after t seconds.
u(t) =

Suppose a mass weighing 64 lb stretches a spring 2 ft. If the
weight is released from rest from 2 ft below the equilibrium
position, find the equation of motion x(t) (using Laplace
transforms) if an impressed force f(t) = 2 sint acts on the system
for 0≤t≤2πand is then removed. Ignore any damping forces.

Q3// The mass-spring-damper system has a 2 kg block is displaced
by an amplitude of 50 mm and
released. If the phase angle of response is 84.17ᴼ, how many cycles
(m) will be executed before
the amplitude is reduced to 1 mm. What are the undamped natural
frequency ωn and spring
constant k if the period of damped oscillation τd is 0.3 sec.

Determine C1 and C2 of the following damped motion
A 4-lb weight stretches a spring 4 ft. Initially the weight
released from 2ft above equilibrium position with downward velocity
2 ft/sec. Find the equation of motion x(t), provided that the
subsequent motion takes place in a medium that offers a damping
force numerically equal to (1/2) times the instantaneous
velocity

A spring of negligible mass stretches 3.00 cm from its relaxed
length when a force of 7.10 N is applied. A 0.440-kg particle rests
on a frictionless horizontal surface and is attached to the free
end of the spring. The particle is displaced from the origin to
x = 5.00 cm and released from rest at t = 0.
(Assume that the direction of the initial displacement is positive.
Use the exact values you enter to make later calculations.)
(a)...

1. Calculate the spring constant ,k, for a spring, if the
spring stretches by 0.2 m as a result of an applied force of
200N.
2. A 20 kg mass is attached to a spring with spring constant,
K=100 N/m. The spring/mass system is stretched by 5cm, and then
released from rest and allowed to oscillate back and forth A.) What
is the amplitude of vibration in this system? B.) Calculate the
acceleration of the mass at X=0.
3. In...

If a mass weighing 40 lbs stretches a spring 6 inches what is
the spring constant? If the mass has a velocity of 4 ft/sec and
this results in a viscous resistance of 68 lbs what is the damping
coefficient? Assume 32lb=1 slug32lb=1 slug
1. suppose the object is displaced upward 8 inches from
equilibrium and released. Create an ODE in terms of the object's
displacement, u(t)u(t) , in feet after tt seconds and
its derivatives and solve for u(t)u(t) .

A mass weighing 24 pounds attached to the end of the spring and
stretches it 4 inches. The mass is initially released from rest
from a point 3 inches above the equilibrium position with a
downward velocity of 2 ft/sec.
Find the equation of the motion?

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