Question

If the displacement of a horizontal mass-spring system was doubled, the elastic potential energy in the system would change by a factor of

Answer 1

K'=4K

Step-by-step explanation:

The electric potential energy is given by :

`E=(1)/(2)kx^2`

Where

k is spring constant

x is compression or extension in the spring

If the displacement of a horizontal mass-spring system is doubled, x'= 2x

New elastic potential energy :

`E'=(1)/(2)kx'^2\\\\E'=(1)/(2)k(2x)^2\\\\=(1)/(2)k* 4x^2\\\\K'=4* (1)/(2)kx^2\\\\K'=4K`

So, new elastic potential energy 4 times the initial elastic potential energy.