Unformatted text preview: MEC702 Wk 7 Tutorial Modeling
1. If a massspring system with an iron ball of weight 98 nt (about 22 lb) can be regarded as
undamped, and the spring is such that the ball stretches it 1.09 m (about 43 in.), how many
cycles per minute will the system execute? What will its motion be if we pull the ball down from
rest by 16 cm (about 6 in.) and let it start with zero initial velocity?
(Solution: y(t) = 0.16 cos 3t)
2. How does the the motion in Question 1 above change if we change the damping constant c from
one to another of the following three values, with y(0) = 0.16 and y 0 (0) = 0 as before?
(a) Case I: c = 100 kg/sec
(b) Case II: c = 60 kg/sec
(c) Case III: c = 10 kg/sec
3. If a weight of 20 nt (about 4.5 lb) stretches a certain spring by 2 cm, what will the frequency of
the corresponding harmonic oscillation be? The period?
4. Show that in the overdamped case, the body can pass through y = 0 at most once.
5. Show that the maxima of an underdamped motion occur at equidistant tvalues and nd the
distance. Higher Order Linear Homoegeneous ODEs
1. Solve the given ODEs.
(a) y 000 + 25y 0 = 0.
(b) y iv + 2y 00 + y = 0.
(c) y iv − 4y 00 = 0.
(d) (D3 − D2 − D + 1)y = 0.
2. Solve the given IVP.
(a) y iv − 9y 00 − 400y = 0, y(0) = 0, y 0 (0) = 0, y 00 (0) = 41, y 000 (0) = 0. (b) 4y 000 + 8y 00 + 41y 0 + 37y = 0, y(0) = 9, y 0 (0) = −6.5, y 00 (0) = −39.75. 1 ...
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 Winter '16
 Alveen Chand
 2 cm, 4.5 lb, 1.09 m, corresponding harmonic oscillation, Linear Homoegeneous ODEs

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