- From the last calculations above we also drew the conclusion that tennis
nd helpful. For horizontal flights from an initial heigh
54) above] the ball can fly a
distance of meters until it reaches the playground
travelling along a nearly straight line provided it has been shot at a speed that is close
ual to 58.3 m/sec. Moreover, it would be better if it flied at a descending trajectory
from the very beginning – shooting above the head from over 1.47 meters height.
9.5 for
and deformations.
y mentioned in (35), (36), (37), when the ball meets the string the force
F causes the tension reactive forces Fa and Fb in the strings. These forces result in a
Load analysis the head and body of the racket and eventual oscillations
ion load on the rim in the direction of the centre of the ellipse of the
frame and also, a bending load in the direction of F and the body (head and handle) of
the racket. If we selected one point M on the body of the racket then these forces
would induce free oscillations with a restoration force of P = - CX, where P is the
restoration force resulting from the elasticity of the construction.
nt is:
The equation for the moveme
If we substitute k =c/m, where k is the natural circular frequency, then
Which represents a second ord
er linear differential equation having constant
icients. Its characteristic second order equation with constant coefficients is r +k
= 0 and both roots are imagin
The differential equation integral is:
X’ = -C1k sinkt +C2kcos t
C1 and C2 are integration constants.
If we substitute C1 = Asinα and C2 = Acosα and A and α are constant, then:
s k.t + cosα . sin k.t) = A sin(k.t + α ).
Therefore, the point A moves harmonically. The constants A and α are
determined using the initial conditions. When t = 0, X = Xo and Vx=Vx,o=Xo and having
differentiated (Eq. 55) we receive:
