Consider a horizontal Spring mass system m attached with a dashpot. The stiffness/ spring constant damping c. Let x(t) denote the position function at time t. is denoted by k, the constant is denoted by 1. A mass on a spring without damping is acted on by the external force F(t) = FO cos^(3) wt. Show that there are two values of w for which resonance occurs, and find both. One can use the formula cos 3t = -3 cost + 4 cos^(3)t, and then rewrite cos^(3)t as a function of cost and cos 3t. 2. If there is no external force and the system is critically damped, show that x(t) = (x0+v0t+ c/(2m)*x0t)e^((- c/2m) t) Here x0 = x(0) and v0 = x'(0) denotes the initial displacement and velocity.
Consider a horizontal Spring mass system m attached with a dashpot. The stiffness/ spring constant damping c. Let x(t) denote the position function at time t. is denoted by k, the constant is denoted by 1. A mass on a spring without damping is acted on by the external force F(t) = FO cos^(3) wt. Show that there are two values of w for which resonance occurs, and find both. One can use the formula cos 3t = -3 cost + 4 cos^(3)t, and then rewrite cos^(3)t as a function of cost and cos 3t. 2. If there is no external force and the system is critically damped, show that x(t) = (x0+v0t+ c/(2m)*x0t)e^((- c/2m) t) Here x0 = x(0) and v0 = x'(0) denotes the initial displacement and velocity.
Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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![Consider a horizontal Spring mass
system m attached with a
dashpot. The stiffness/ spring
constant is denoted by k, the
damping constant is denoted by
c. Let x(t) denote the position
function at time t.
1. A mass on a spring without
damping is acted on by the
external force F(t) = FO cos^(3) wt.
Show that there are two values of
w for which resonance occurs,
and find both.
=
One can use the formula cos 3t
-3 cost + 4 cos^(3)t, and then
rewrite cos^(3)t as a function of
cost and cos 3t.
2. If there is no external force and
the system is critically damped,
show that x(t) = (x0+v0t+
c/(2m)*x0t)e^((- c/2m) t)
Here x0 = x(0) and v0 = x'(0)
denotes the initial displacement
and velocity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F699ae69d-2801-4824-8f3f-ea4103b997bd%2F2a810c40-f602-4d65-b486-d162a70fdba1%2Fllgdfrm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a horizontal Spring mass
system m attached with a
dashpot. The stiffness/ spring
constant is denoted by k, the
damping constant is denoted by
c. Let x(t) denote the position
function at time t.
1. A mass on a spring without
damping is acted on by the
external force F(t) = FO cos^(3) wt.
Show that there are two values of
w for which resonance occurs,
and find both.
=
One can use the formula cos 3t
-3 cost + 4 cos^(3)t, and then
rewrite cos^(3)t as a function of
cost and cos 3t.
2. If there is no external force and
the system is critically damped,
show that x(t) = (x0+v0t+
c/(2m)*x0t)e^((- c/2m) t)
Here x0 = x(0) and v0 = x'(0)
denotes the initial displacement
and velocity.
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