Respuesta :
The time period of the spring - mass system undergoing simple harmonic motion is 5.024 seconds.
We have a mass weighing 16 pounds which is attached to a spring whose spring constant is 25 lb/ft . This complete spring - mass system is undergoing simple harmonic motion.
We have to calculate the time period of this simple harmonic motion.
What is the formula to calculate the Time period of a spring - mass system performing Simple harmonic motion?
The formula to calculate the time period of a spring - mass system undergoing simple harmonic motion is -
[tex]T=2\pi \sqrt{\frac{m}{k} }[/tex]
Where -
T is the time period of spring - mass simple harmonic motion.
m is the mass of body
k is the spring constant
In the question given -
mass (m) = 16 pounds
Spring constant (k) = 25 lb/ft
Substituting the values in the formula above -
T = [tex]2\pi \sqrt{\frac{16}{25} }[/tex] = [tex]\frac{2\pi \times4}{5}[/tex] = 5.024 seconds
Hence, the time period of the spring - mass system undergoing simple harmonic motion is 5.024 seconds.
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