How will the period of oscillation of a spring pendulum change with an increase
| September 1, 2021 | education
How will the period of oscillation of a spring pendulum change with an increase in the spring stiffness by 4 times and a decrease in the weight of the load by 4 times?
Oscillation period:
T = 2Π * √ (m / k), m is the mass of the load, k is the stiffness of the spring.
Before increasing the spring stiffness by 4 times and reducing the mass by 4 times:
T1 = 2Π * √ (m1 / k1).
After increasing the spring stiffness by 4 times and reducing the mass by 4 times:
T2 = 2Π * √ (m2 / k2), m2 = 1/4 m1 = 0.25 m1, k2 = 4k1.
Т2 / Т1 = 2Π * √ (m2 / k2) / 2Π * √ (m1 / k1) = √ (0.25m1 / 4k1) / √ (m1 / k1) = √ (m1 / 16k1) / √ (m1 / k1 ) = 1/4.
Answer: The oscillation period will decrease by 4 times.
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