Question

A spring with a spring constant of 25.1 N/m is attached to different masses, and the system is set in motion. What is its period for a mass of 3.0 kg? Answer in units of s. 003 (part 2 of 6) 10.0 points What is its frequency? Answer in units of Hz. 004 (part 3 of 6) 10.0 points What is the period for a mass of 11 g? Answer in units of s. 005 (part 4 of 6) 10.0 points What is its frequency? Answer in units of Hz. 006 (part 5 of 6) 10.0 points What is the period for a mass of 1.6 kg?

Answer 1

1) 2.17 s

The period of a mass-spring oscillating system is given by

$T=2 \pi \sqrt{\frac{m}{k}}$

where k is the spring constant and m is the mass attached to the spring. In this problem, we have

k = 25.1 N/m

m = 3.0 kg

Substituting into the equation, we find

$T=2 \pi \sqrt{\frac{3.0 kg}{25.1 N/m}}=2.17 s$

2) 0.46 Hz

The frequency of the oscillating system is equal to the reciprocal of the period:

$f=\frac{1}{T}$

Therefore, by substituting T=2.17 s, we find:

$f=\frac{1}{T}=\frac{1}{2.17 s}=0.46 Hz$

3) 0.13 s

As before, the period of a mass-spring oscillating system is given by

$T=2 \pi \sqrt{\frac{m}{k}}$

where k is the spring constant and m is the mass attached to the spring. In this part of the problem, we have

k = 25.1 N/m

m = 11 g = 0.011 kg

Substituting into the equation, we find

$T=2 \pi \sqrt{\frac{0.011 kg}{25.1 N/m}}=0.13 s$

4) 7.69 Hz

The frequency of the oscillating system is equal to the reciprocal of the period:

$f=\frac{1}{T}$

Therefore, by substituting T=0.13 s, we find:

$f=\frac{1}{T}=\frac{1}{0.13 s}=7.69 Hz$

5) 1.59 s

Again, the formula for the period of a mass-spring oscillating system is given by

$T=2 \pi \sqrt{\frac{m}{k}}$

In this part of the problem, we have

k = 25.1 N/m

m = 1.6 kg

Substituting into the equation, we find

$T=2 \pi \sqrt{\frac{1.6 kg}{25.1 N/m}}=1.59 s$