Springs in Parallel and in Series

connected in

series

parallel

number of springs

2

3

Δx

1.

k

1

2.

k

2

2.

k

3

3.5

m

3

k

E

= 7.50 N/m | F = 7.50 N | T = 3.97 s

A vibrating system with a mass

m

(orange) attached with more than one spring can be arranged either in series or in parallel. The spring constants are

k

1

,

k

2

, and

k

3

and the equivalent spring constant is

k

E

. Using Hooke's law, the period

T

of the system and the force are calculated for a displacement

Δx

.

Details

For springs in parallel

k

E

=

k

1

+

k

2

+

k

3

; in series

k

E

=

-1

(1/

k

1

+1/

k

2

+1/

k

3

)

. In either case,

T=2π

m/

k

E

.

External Links

Spring (ScienceWorld)

Spring Constant (ScienceWorld)

Hooke's Law (ScienceWorld)

Springs—Two Springs in Series (ScienceWorld)

Springs—Two Springs in Parallel (ScienceWorld)

Period (ScienceWorld)

Permanent Citation

Enrique Zeleny

"Springs in Parallel and in Series"
http://demonstrations.wolfram.com/SpringsInParallelAndInSeries/
Wolfram Demonstrations Project
Published: October 29, 2010