Energy in SHM

In a system w/o friction the total mechanical energy is constant

Remember: In a system w/o friction the total mechanical energy is constant

E = K + U = ½ k A²

Equation for total energy:

E is continuously being transferred btw U and KE but overall the total E is constant (E is conserved)

Remember: E is continuously being transferred btw U and KE but overall the total E is constant (E is conserved)

x = -A or A (end points of the motion)

@ what positions would the block be stuck and all Energy is U?

x = 0

@ what position would the spring be @ its equilibrium position and all Energy is KE?

on a swing/pendulum potential energy is not elastic, it is gravitational (Ug)

Remember: on a swing/pendulum potential energy is not elastic, it is gravitational (Ug)

conservation of E can be used to find the velocity @ any position x (E = K + U)

Remember: conservation of E can be used to find the velocity @ any position x (E = K + U)

½ k A² = ½ m v² + ½ k x²

E = K + U equation to solve for V:

ω = √k/m

remember: ω = √k/m

friction and drag

what are two non-conservative forces?

they cause energy to be dissipated out of the system as heat (thermal energy)

what do non-conservative forces cause in real life?

Damped

• Def: mechanical E of the system diminishes in time

• Amplitude (A) & envelope decays exponentially during these types of oscillations

Ae^-t/T

amplitude or envelope during damped oscillations:

x(t) = Ae^-t/ cos (ωt + ∅)

equation for position during damped oscillations:

the amplitude has decreases to approx. 37% of its initial value

when t = T?

the amplitude has decreased to approx. 13% of its initial value

when t = 2T?

The stronger (more) damping, the smaller the time constant, & the faster the amplitude decreases

Remember: The stronger (more) damping, the smaller the time constant, & the faster the amplitude decreases