A 1.30 kg mass is suspended from a spring, with a spring constant of 135.0 N/m. Find the driving frequency which would cause resonance.
Do a Google search for " natural frequency of spring mass system"
You should know it by heart.
I know that w=squ(k/m)
and T=(2*pai)/w
but its wrong and I don't know what to do.. can you help me?
To find the driving frequency that would cause resonance, we need to understand the concept of resonance and the formula for calculating the resonant frequency for a mass-spring system.
Resonance occurs when the driving frequency matches the natural frequency of the system, resulting in maximum amplitude of oscillation. In a mass-spring system, the natural frequency (ω0) is given by the formula:
ω0 = √(k / m)
Where:
- ω0 is the natural frequency in radians per second (rad/s)
- k is the spring constant in Newtons per meter (N/m)
- m is the mass in kilograms (kg)
In our case, the mass (m) is given as 1.30 kg, and the spring constant (k) is given as 135.0 N/m.
Let's substitute these values into the formula to calculate the natural frequency:
ω0 = √(135.0 N/m / 1.30 kg)
= √(103.846)
≈ 10.19 rad/s
We have now found the natural frequency of the system. To find the driving frequency for resonance, we set the driving frequency (ωd) equal to the natural frequency (ω0):
ωd = ω0
= 10.19 rad/s
Therefore, the driving frequency which would cause resonance is approximately 10.19 rad/s.