The Linear Spring-Mass System

Classical Mechanics Level 4


A Mass m \displaystyle m is attached to a spring of mass M \displaystyle M and spring constant K \displaystyle K .

If the velocity of the mass m \displaystyle m varies linearly when it is given a kick, Let T \displaystyle T denote the Time Period of the system.

Find 1000 T \displaystyle 1000T to the nearest integer.

Details and Assumptions:
∙ m = 3 K g \bullet m = 3Kg
∙ M = 0.5 K g \bullet M = 0.5Kg
∙ K = 100 N / m \bullet K = 100N/m


The answer is 1118.

Anish Puthuraya by Anish Puthuraya , 24, India

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2 solutions

Here you can find the complete solution of this kind of problem: http://www.luiseduardo.com.br/undulating/SHM/springwithmass.htm

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Anandhu Raj - 5 years, 2 months ago
Rab Gani
Jan 19, 2019

For spring with mass M, we can calculate the angular velocity ω = √(k/(m+(1/3)M)). So ω=5.6195 rad/s. And ω= 2π /T, Then T=1.1181 s. So 1000T = 1118

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