Question

A 8.15 kg mass oscillates up and down on a spring that has a force constant of 90 N/m.

(a) What is the angular frequency of this spring/mass system (in rad/s)?
(b) What is the period of this spring/mass system (in seconds)?

Answer 1

The angular frequency of the spring/mass system is 3.96 rad/s, and the period is 1.59 s.

Step-by-step explanation:

The angular frequency (ω) of the spring/mass system can be calculated using the formula:

ω = √(k/m)

where k is the force constant of the spring and m is the mass of the object.

Plugging in the given values:

ω = √(90 N/m / 8.15 kg) = 3.96 rad/s

The period (T) of the spring/mass system can be calculated using the formula:

T = 2π/ω

Plugging in the angular frequency obtained:

T = 2π / 3.96 rad/s = 1.59 s

Answer 2

(a) The angular frequency ($\omega$) of a spring/mass system with a force constant ($k$) and a mass ($m$) can be found using the formula:

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

Plugging in the values given, we get:

\omega = \sqrt{\frac{90 N/m}{8.15 kg}} \approx 3.18 \text{ rad/s}

Therefore, the angular frequency of the spring/mass system is approximately 3.18 rad/s.

(b) The period ($T$) of a spring/mass system can be found using the formula:

T = \frac{2\pi}{\omega}

Plugging in the value of $\omega$ we found in part (a), we get:

T = \frac{2\pi}{3.18\text{ rad/s}} \approx 1.98 \text{ s}

Therefore, the period of the spring/mass system is approximately 1.98 s.