Simple Harmonic Motion Problems

[mustang]

Problem 3.
A 127 N object vibrates with a period of 3.45 s when hanging from a spring.
The acceleration of gravity is 9.81 m/s^2.
What is the spring constant of the spring?
Answer in N/m.
Note: How would one solve this type of problem?

Problem 8.
A spring with a spring constant of 28.9 N/m is attached to different masses, and the system is set into motion.
What is its frequendy? In Hz.
Note: WHat formula do I use?

Problem 13.
A paino emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz.
Find the maximum wavelength in air attained by this instrument when the speed of sound in air is 344m/s. In m.
Note: WHat formula do I use?

Problem 21.
Microwaves travel at the speed of light, 3*10^8m/s.
When the frequency of microwaves is 7.35*10^9 Hz, what is their wavelength? In m.

 

[HallsofIvy]

Originally posted by mustang
Problem 3.
A 127 N object vibrates with a period of 3.45 s when hanging from a spring.
The acceleration of gravity is 9.81 m/s^2.
What is the spring constant of the spring?
Answer in N/m.
Note: How would one solve this type of problem?

Perhaps by knowing that an object of mass m hanging from a spring with spring constant k vibrates with a period given by $$2\pi\sqrt{\frac{m}{k}}$$.
One problem with not showing any attempt to do a problem at all is that we don't know what you do know in order to help you.

Problem 8.
A spring with a spring constant of 28.9 N/m is attached to different masses, and the system is set into motion.
What is its frequendy? In Hz.
Note: WHat formula do I use?

Same as the previous problem.

Problem 13.
A paino emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz.
Find the maximum wavelength in air attained by this instrument when the speed of sound in air is 344m/s. In m.
Note: WHat formula do I use?

If you honest don't know and cannot look up the relationship between "frequency" and "wavelength" then you should not be taking this course!

Problem 21.
Microwaves travel at the speed of light, 3*10^8m/s.
When the frequency of microwaves is 7.35*10^9 Hz, what is their wavelength? In m.

Once again: what is the relationship between frequency and wavelength of any wave?

 

[M98Ranger]

In order to solve Problem 3, one would use the formula T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. In this case, T is given as 3.45 s and m is given as 127 N. Rearranging the formula to solve for k, we get k = 4π^2m/T^2. Plugging in the values, we get k = 4π^2(127 N)/(3.45 s)^2 = 73.82 N/m. Therefore, the spring constant of the spring is 73.82 N/m.

To solve Problem 8, we would use the formula f = 1/2π√(k/m), where f is the frequency, k is the spring constant, and m is the mass. In this case, k is given as 28.9 N/m. We can rearrange the formula to solve for f, which gives us f = 1/2π√(28.9 N/m)/(m). Since the mass is not given, we cannot solve for the frequency. The formula for frequency is also known as the natural frequency of the system.

For Problem 13, we would use the formula λ = v/f, where λ is the wavelength, v is the speed of sound, and f is the frequency. In this case, v is given as 344 m/s and the frequency range is given as 28 Hz to 4200 Hz. To find the maximum wavelength, we need to find the minimum frequency, which is 28 Hz. Plugging in the values, we get λ = (344 m/s)/(28 Hz) = 12.29 m. Therefore, the maximum wavelength achieved by the piano is 12.29 m.

Finally, for Problem 21, we would use the formula λ = c/f, where λ is the wavelength, c is the speed of light, and f is the frequency. In this case, c is given as 3*10^8 m/s and f is given as 7.35*10^9 Hz. Plugging in the values, we get λ = (3*10^8 m/s)/(7.35*10^9 Hz) = 0.0408 m. Therefore, the wavelength of microwaves with a frequency of 7.35*10