Statement#

A mass $m$ is attached to a spring with spring constant $k$ and can move horizontally without friction. The spring obeys Hooke's law: $F = -kx$.

1. Derive the equation of motion for the mass
2. Solve the differential equation to find $x(t)$, the position as a function of time
3. Express the solution in terms of the angular frequency $\omega = \sqrt{k/m}$

Required Topics#

• Newton's second law
• Hooke's law
• Second-order linear differential equations
• Initial conditions
• Simple harmonic motion

Given Information#

• Mass: $m$
• Spring constant: $k$
• Restoring force: $F = -kx$ (Hooke's law)
• Initial position: $x(0) = x_0$
• Initial velocity: $v(0) = v_0$

What to Find#

1. The differential equation: $m\frac{d^2x}{dt^2} + kx = 0$
2. General solution: $x(t)$ in terms of $\omega$, $x_0$, and $v_0$
3. The period of oscillation $T$

Solution#

Solution coming soon.