Question

1. A 2 kg mass hangs from a spring with Hooke's law constant $k = 8$ and is attached to a driving force $F = F_0sin(\omega_0 t)$. (a) Show that only the driving angular frequency $\omega = 2$ will cause resonance and find the general solution for the motion when $\omega = 2$ and $F_0 = 8$. (b) If $\omega_0 = 1$ and $F_0 = -6$ find general solution for the motion of the mass for $t > 0$ as a sum of sine waves of different frequencies.

          1.
A 2 kg mass hangs from a spring with Hooke's law constant $k = 8$ and is attached to a driving
force $F = F_0sin(\omega_0 t)$.
(a) Show that only the driving angular frequency $\omega = 2$ will cause resonance and find the
general solution for the motion when $\omega = 2$ and $F_0 = 8$.
(b) If $\omega_0 = 1$ and $F_0 = -6$ find general solution for the motion of the mass for $t > 0$ as a sum of
sine waves of different frequencies.

1.
A 2 kg mass hangs from a spring with Hooke's law constant k = 8 and is attached to a driving
force F = F0sin(ω0 t).
(a) Show that only the driving angular frequency ω = 2 will cause resonance and find the
general solution for the motion when ω = 2 and F0 = 8.
(b) If ω0 = 1 and F0 = -6 find general solution for the motion of the mass for t > 0 as a sum of
sine waves of different frequencies.

Added by Melissa V.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sam Stansfield

Step 1

The natural angular frequency, ω0, is given by the formula: ω0 = √(k/m) where k is the Hooke's law constant and m is the mass. In this case, k = 8 and m = 2, so ω0 = √(8/2) = √4 = 2. For resonance to occur, the driving angular frequency, ω, must be equal to the Show more…

Show all steps

Thanks for your feedback!

A 2 kg mass hangs from a spring with Hooke's law constant k = 8 and is attached to a driving force F = Fosin(Ï‰t). (a) Show that only the driving angular frequency Ï‰ = 2 will cause resonance and find the general solution for the motion when Ï‰ = 2 and F = 8. (b) If Ï‰ = 1 and Fo = -6, find the general solution for the motion of the mass for t > 0 as a sum of sine waves of different frequencies.