Question

In: Advanced Math

A spring with a spring constant 4 N/m is loaded with a 2 kgmass and allowed...

A spring with a spring constant 4 N/m is loaded with a 2 kgmass and allowed to reach equilibrium. It is then displaced 1 meter downward and released. Suppose the mass experiences a damping force in Newtons equal to 1 times the velocity at every point and an external force of F(t)=4sin(3t) driving the system. Set up a differential equation that describes this system and find a particular solution to this non-homogeneous differential equation:

Solutions

Expert Solution

spring constant

mass

damping force in Newtons equal to 1 times the velocity

so damping constant is

external force is

.

DE is given by

....................differential equation for this system

.

in question mention that, find an only a particular solution

.

here we have so assume that particular solution is

....................(1)

.

put all values in DE

.

.

.

compare coefficient both sides

....................put both constants in equation 1

.

...................... particular solution

Colby Messinger answered 2 years ago
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