Question

A 0.200 kg mass is attached to a horizontal spring and oscillates such that its position vs. time plot is given below. x( Im) 1.0 r 0.5 0.0 0.5 1.0 .5 2.0 -0.5 -10L (a) What is the period of motion? 1.5 (b) What is the angular frequency? 4.18879rad/s (c) What is the spring constant of the spring? 3.5091923 N/m (d) What is the fastest speed the mass attains? 1.5 m/s (e) What is the total mechanical energy of the system? 0.631654614

Answer 1

(a) Period of the motion is the time required to complete one oscillation i.e. one crest and trough Which completes at soT =1.5 s

(b) the frequency f = 1/T = 0.6667

the angular frequency is given by $\omega = 2\pi f = 2 \times 3.14 \times 0.6667 = 4.1867rad/s$

(c) the spring constant is given by

$k = m\omega ^{2} = 0.2 \times (4.1867)^{2} = 3.5056 N/m$

(d) fastest speed is v = dx/dt = 0.6/0.4 = 1.5 m/s

e) the total mechanical energy is given by

$T = \frac{1}{2}m\omega ^{2}a^{2}$

$T = \frac{1}{2}\times 0.2\times(4.1867) ^{2}(0.6)^{2}$

$T = 0.6310 J$