Question
In: Advanced Math
(10pts) Consider the damped forced harmonic oscillator with mass 1 kg, damping coefficient 2, spring constant...
- (10pts) Consider the damped forced harmonic oscillator with mass 1 kg, damping coefficient 2, spring constant 3, and external force in the form of an instantaneous hammer strike (Section 6.4) at time t = 4 seconds. The mass is initially displaced 2 meters in the positive direction and an initial velocity of 1 m/s is applied. Model this situation with an initial value problem and solve it using the method of Laplace transforms.
Solutions
Colby Messinger answered 2 years agoRelated Solutions
Consider the undamped forced harmonic oscillator with mass 1 kg, damping coefficient 0, spring constant 4,...
Consider the undamped forced harmonic oscillator with mass 1
kg, damping coefficient 0, spring constant 4, and external force
h(t) = 3cos(t). The mass is initially at
rest in the equilibrium position. You must understand that you can
model this as: y’’ = -4y +3cost;
y(0) = 0; y’(0) = 0.
(5pts) Using the method of Laplace transforms, solve this
initial value problem.
Check your solution solves the IVP.
(4pts) Be sure to check that your solution satisfies both the...
1.For a damped simple harmonic oscillator, the block has a mass of 2.3 kg and the...
1.For a damped simple harmonic oscillator, the block has a mass
of 2.3 kg and the spring constant is 6.6 N/m. The damping force is
given by -b(dx/dt), where b =
220 g/s. The block is pulled down 12.4 cm and released.
(a) Calculate the time required for the amplitude
of the resulting oscillations to fall to 1/8 of its initial value.
(b) How many oscillations are made by the block in
this time?
2.An oscillator consists of a block...
Consider a classical harmonic oscillator of mass m and spring constant k . What is the...
Consider a classical harmonic oscillator of mass
m
and spring constant
k
. What is the probability
density for finding the particle at position
x
? How does this compare to the probability density for
the ground state of a quantum mechanical harmonic oscillator
Consider a damped forced mass-spring system with m = 1, γ = 2, and k =...
Consider a damped forced mass-spring system with m = 1, γ = 2,
and k = 26, under the influence of an external force F(t) = 82
cos(4t).
a) (8 points) Find the position u(t) of the mass at any time t,
if u(0) = 6 and u 0 (0) = 0
. b) (4 points) Find the transient solution uc(t) and the steady
state solution U(t). How would you characterize these two solutions
in terms of their behavior in...
A spring with a mass of 1 kg has damping constant 10 kg/s and a spring...
A spring with a mass of 1 kg has damping constant 10 kg/s and a
spring constant 41 kg/s2 . If the spring begins at equilibrium
position and is given a velocity of 2 m/s, find the position of the
mass at any time t. Is this overdamping, critical damping or
underdamping?
A spring with a mass of 1 kg has damping constant 10 kg/s and a spring...
A spring with a mass of 1 kg has damping constant 10 kg/s and a
spring constant 41 kg/s2 . If the spring begins at equilibrium
position and is given a velocity of 2 m/s, find the position of the
mass at any time t. Is this overdamping, critical damping or
underdamping?
A spring with a mass of 2 kg has a damping constant 14 kg/s. A force...
A spring with a mass of 2 kg has a damping constant 14 kg/s. A
force of 3.6 N is required to keep the spring stretched 0.3 m
beyond its natural length. The spring is stretched 0.7 m beyond its
natural length and then released. Find the position of the mass at
any time t. (Assume that movement to the right is the
positive x-direction and the spring is attached to a wall
at the left end.) What is x(t)?
A spring with 2 kg mass has damping constant 14 and a force of 6 Newton...
A spring with 2 kg
mass has damping constant 14 and a force of 6 Newton is required to
keep the spring stretched 0.5 meter beyond its natural length. The
spring is stretched 1 meter beyond its natural length and then is
released with zero initial velocity. If an external force of F(t)=
2sin2t is applied to the system, find the position of the mass at
any time t.
A simple harmonic oscillator consists of a block of mass 3.70 kg attached to a spring...
A simple harmonic oscillator consists of a block of mass 3.70 kg
attached to a spring of spring constant 260 N/m. When t = 1.60 s,
the position and velocity of the block are x = 0.199 m and v =
3.920 m/s. (a) What is the amplitude of the oscillations? What were
the (b) position and (c) velocity of the block at t = 0 s?
A simple harmonic oscillator consists of a block of mass 3.4 kg attached to a spring...
A simple harmonic oscillator consists of a block of mass 3.4 kg
attached to a spring of spring constant 120 N/m. When t =
0.84 s, the position and velocity of the block are x =
0.127 m and v = 3.23 m/s. (a) What is the
amplitude of the oscillations? What were the (b)
position and (c) velocity of the block at
t = 0 s?
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