Question

ou want to predict the frequency with which a ball-on-spring system will oscillate. You measure the spring constant to be 193 N/m and use a ball of mass 1.26 kg. What is the frequency (in Hz)? Enter answer here 19.4 Hz

Answer 1

Answer:

$f=1.97Hz$

Explanation:

The angular frequency of a mass-spring system is defined as:

$\omega=\sqrt{\frac{k}{m}}$

Here k is the spring constant and m is the mass of the ball. So, replacing the given values:

$\omega=\sqrt{\frac{193\frac{N}{m}}{1.26kg}}\\\omega=12.38\frac{rad}{s}$

The frequency is directly proportional to the angular frequency, as follows:

$f=\frac{\omega}{2\pi}\\f=\frac{12.38\frac{rad}{s}}{2\pi}\\f=1.97Hz$