Initial Value Problems - Numerical Methods in Engineering with MATLAB - page 269

Use numerical integration to determine the period of the pendulum if the am pli-
tude is π L g .

8. A skydiver of mass m in a verticalfree fall experiences an aerodynamic drag
force F D =

θ 0 = 1 rad. Note thatfor small amplitudes (sin θ ≈ θ ) the periodis 2 /

c D y 2 , where y is measureddownward from the start of the fall. The
differentialequationdescribing the fall is

c D
m y 2

y = g −

80665 m/s 2 , c D = Determine the timeofa500 m fall. Use g = 9 . 0 . 2028 kg/m and

m = 80kg.

9.

y

k

P ( t )

m

The spring-mass systemis at rest when the force P ( t ) is applied, where

10 t N when t

< 2 s

P ( t ) =

20N when t ≥ 2 s

The differentialequation for the ensuing motionis

k
m y
Determine the maximum displacement of the mass. Use m

P ( t )
m −

y =

= 2 . 5 kg and k =

75 N/m.
10.

Water level

y

The conical float isfree to slideonavertical rod. When the float is disturbed
fromits equilibrium position, it undergoes oscillating motiondescribedbythe
differentialequation

g 1 ay 3 y = −