A 1.35 kg mass is suspended from a spring with a spring constant of 189.0 N/m. The spring is attached to a rod which oscillates vertically at a frequency f. For what value of the frequency f will the system resonate?
Same question as the one below. Please look it up.
To find the value of the frequency at which the system resonates, we need to understand the concept of resonance and how it relates to the natural frequency of the system.
Resonance occurs when an external force is applied to a system at its natural frequency, causing the amplitude of the system's oscillations to be maximized. In the case of a mass-spring system, the natural frequency is determined by the mass of the object and the spring constant.
The natural frequency of a mass-spring system can be found using the formula:
f = 1 / (2π) * sqrt(k / m)
where f is the natural frequency, k is the spring constant, and m is the mass.
Given that the mass (m) is 1.35 kg and the spring constant (k) is 189.0 N/m, we can calculate the natural frequency of the system:
f = 1 / (2π) * sqrt(189.0 / 1.35)
f = 5.65 Hz
Therefore, the natural frequency of the system is 5.65 Hz.
In order for the system to resonate, the frequency at which the rod oscillates (f) must match the natural frequency of the system. So the value of the frequency (f) at which the system resonates is 5.65 Hz.