EXAMPLES XXI 878 



d?x 



(\"2) -j^ = 2(Xr, where x ft. is distance and i sees, is time, repre- 

 sents the equation of motion of a body. Find an expression 

 giving x in terms of t when the initial conditions are : (1) t = 0, 



//I* //'T* 



a? - 0-5, and -j- = ; (2) t = 0, x = 0, and ^ = 4 ; (8) / = 0, 



, dx 



x = 0-5. and -p = 4. 

 at 



d?x dx 



(13) -T-J + 4 -T- + 20# = 0, where x ft. is distance and t sees, is 



time, represents the equation of motion of a body. Find an 

 expression giving x in terms of t when the initial conditions are: 



/7"? 1 //"7 1 



(1) t = 0, x = 0-5, and -f- = ; (2) t = 0, a; = 0, and -77 = 4 ; 



ul uf 



/7*? 1 



(3) t = 0, a; = 0-5, and -^- = 4. What is the periodic time of the 



motion ? 



d z x dx 



(14) -5-5 + 4-j- + 4# = 0, where rr ft. is distance and t sees, is 



( // f / ' 



time, represents the equation of motion of a body. Find an 

 expression giving x in terms of t when the initial conditions are : 



f7"7* (Lt^T 



(1) t = 0, a; = 0-5, and -5- = ; (2) t = 0, x = 0, and ^- = 4 ; 



d0 



(3) t = 0, a; = 0-5, and -7- = 4. In each case find the maximum 



wZ 



value of x and the time at which it occurs. 



d 2 x dx 



(15) -7-5 + 4-r- + 3x = 0, where # ft. is distance and t sees, is 



M / '/( \ 



time, represents the equation of motion of a body. Find an 

 expression giving x in terms of t when the initial conditions are : 



(l*X* (L3T 



(1) t = 0, x= 0-5, and -3- = ; (2) t = 0, x = 0, and -3- - 4 ; 



cfo? 

 (3) t = 0, # = 0-5, and = 4. In each case find the maximum 



0v 



value of # and the time at which it occurs. 



(16) A force of 10 Ib. extends a spring by 1-6 inches. A mass 

 of 8 Ib. is suspended from such a spring and is displaced 2 inches 

 from its equilibrium position and then let go. If x ft. is the 

 distance of the mass from the equilibrium position at any sub- 

 sequent time, t sees, find the equation of motion for the body 

 and then find an expression giving x in terms of t. What is the 

 periodic time of the motion and how many complete oscillations 

 does the body make per minute ? (g = 32-2 f.s.s.) 



