While determining the potential energy stored in a spring–mass system executing SHM

PHYSICS · Single correct · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

While determining the potential energy stored in a spring–mass system executing SHM, the work done in moving the mass from

x = 0

x

is expressed as an integral. Which of the following integrals correctly represents this work (and hence the potential energy)? (a)

\displaystyle \int_{0}^{x} -kx'\,dx'

(b)

\displaystyle \int_{0}^{x} \tfrac{kx'}{2}\,dx'

(c)

\displaystyle \int_{0}^{x} 2kx'\,dx'

(d)

\displaystyle \int_{0}^{x} kx'\,dx'