Intro to Simple Harmonic Motion (Horizontal Springs) Video Lessons

Concept

# Problem: Suppose you have a mass m attached to a spring constant k (N/m). The mass rests on a horizontal frictionless surface. Its equilibrium position is at x= 0. It is pulled aside a distance A and released.a) What is its speed as it passes the position x=0?b) What is the net force on the mass at position x=A?c) Do you expect the mass to have SHM?d) What is its speed when x=A/4?

###### FREE Expert Solution

a)

From the law of conservation of energy:

$\overline{)\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{A}}}^{{\mathbf{2}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

Solving for v:

$\begin{array}{rcl}\overline{)\frac{\mathbf{1}}{\mathbf{2}}}{{\mathbf{mv}}}^{{\mathbf{2}}}& \mathbf{=}& \overline{)\frac{\mathbf{1}}{\mathbf{2}}}{{\mathbf{kA}}}^{{\mathbf{2}}}\\ \mathbf{v}& \mathbf{=}& \sqrt{\frac{\mathbf{k}}{\mathbf{m}}{\mathbf{A}}^{\mathbf{2}}}\end{array}$

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###### Problem Details

Suppose you have a mass m attached to a spring constant k (N/m). The mass rests on a horizontal frictionless surface. Its equilibrium position is at x= 0. It is pulled aside a distance A and released.

a) What is its speed as it passes the position x=0?

b) What is the net force on the mass at position x=A?

c) Do you expect the mass to have SHM?

d) What is its speed when x=A/4?