Damping is negligible for a 0.135-kg object hanging from a light, 6.30-n/m spring. a sinusoidal force with an amplitude of 1.70 n drives the system. at what frequency will the force make the object vibrate with an amplitude of 0.480 m?

0.72 Hz minimum frequency

Explanation:

When the damping is negligible,Amplitude is given as

here = (6.30)/(0.135) = 46.67 N/m kg

= 1.70/(0.135)(0.480) = 26.2 N/m kg

From the above equation , rearranging for ω,

⇒ ω² =46.67 ± 26.2 = 72.87 or 20.47

⇒ ω = 8.53 or 4.52 rad/s

Frequency = f

ω=2 π f

⇒ f = ω / 2π =  8.53 /6.28  or 4.52 / 6.28 = 1.36 Hz or 0.72 Hz

The lower frequency is 0.72 Hz and higher is 1.36 Hz

this means that the temperature of both substances will be equal