- #1

LCSphysicist

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- Homework Statement
- All below

- Relevant Equations
- All below

The displacement of the end of a spring varies as
, the block on the spring is subject to a viscous force proportional to the velocity. Spring stiffness k.

(a)Find the displacement of the block:

(b)When γ -> 0

First of all, i have a doubt i we could start saying the component of the force is the imaginary component, seems plausible?

Anyway:

## x'' + yx' + wo²*x = wo²*d*sin(wt) ##

## sin(wt) = cos(wt + 3pi/2) ## , x is Real part of z

## z'' + yz' + wo²z = wo²*d*e^{(wt + 3pi/2)i} ##

## Solving for z = A*e^{i(wt + 3pi/2)) ##

(a)X=
+

(b)X =
+

That's ok?

(a)Find the displacement of the block:

(b)When γ -> 0

First of all, i have a doubt i we could start saying the component of the force is the imaginary component, seems plausible?

Anyway:

## x'' + yx' + wo²*x = wo²*d*sin(wt) ##

## sin(wt) = cos(wt + 3pi/2) ## , x is Real part of z

## z'' + yz' + wo²z = wo²*d*e^{(wt + 3pi/2)i} ##

## Solving for z = A*e^{i(wt + 3pi/2)) ##

(a)X=

(b)X =

That's ok?

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