Hooke's law: an ideal spring exerts a force which is proportional to the distance the spring is moved from the equilibrium and experiences no energy loss due to friction, $\overrightarrow F_s = -k \triangle \overrightarrow x$

$W=\frac{1}{2}k(\triangle x)^2$

• The force exerted by a spring is a restorative force
  • Acts in the opposite direction of the displacement to return the spring to its natural length
• The constant of proportionality in Hooke's law is the spring constant, k.
  • The spring constant is large when a spring is stiff and small when a spring is loose
  • Measured in newtons per metre
• The energy stored in an object that is stretched, compressed, twisted or bent is called elastic potential energy, $E_e = \frac{1}{2}k(\triangle x)^2$

Simple harmonic motion is periodic motion in which an object moves in response to a force that is directly proportional and opposite to its displacement

• For uniform motion with a period, T (A is amplitude)

  $a_c = \frac{4\pi^2r}{T^2}$

  $T = 2\pi \sqrt{\frac{A}{a_c}}$

• Period of mass on a spring

  $T =2\pi \sqrt{\frac{m}{k}}$

• Use Hooke's law and Newton's second law to calculate the acceleration of the mass

  $\overrightarrow F_x = -k \triangle \overrightarrow x$

  $\overrightarrow F_x = m \overrightarrow a_x$

  $k \triangle \overrightarrow x = m \overrightarrow a_x$

PHeT Hooke’s Law Simulation

2.)

Known variables

$\triangle \overrightarrow x = 8$cm = 0.04m

$m$ = 50g = 0.05kg

$a = g = 9.8 \frac{m}{s^2}$

$k \triangle \overrightarrow x = m \overrightarrow a_x$

$k = \frac{ma}{\triangle x}$