918 
rT : q E sin wt = cos ot + il H(t) (1-28) 
9° 
To obtain maximum deformation: 
[Foon ate + vin aty = be¥9| =0 
M 3 
My 
9” . 
etn /? = cos wt, + o@ sin ot, (I-29) 
The time of maximum deformation, t,, must be obtained by solving Eq. (I-29). 
Since this is a transcendental equation, the solution must be carried out 
graphically or by successive approximation.» A new solution is required for 
each new value of 0. 
Putting Eqe (I-29) into Eq. (I-28) : 
2 
Fo 1 Fo 
2 | — sin wot, + 00 sin wo = — sin o 
™ M(1 + w® 02) fe tn ts | on tn 
and hence 
2F wo 
= — — sin wo I-30 
*n Onna |} *n ( 
The relative response ¥ is therefore: 
ae 
x = =z sin ot, (I-31) 
Generalized plots of ¥ and wt,/n ve. 0 are given in Fig. I-4- Plots 
of ¥ and t, vs- © for 5/32 in. and 3/8 in. balls used under water are given 
in Figs- I-5 and I-66 
-103-= 
