Strona0289

289

> V: = V [ 1 ] +V [ 2 ] ;

V := -mgx(0 Ąk{S„ + x(/))² ~kSl

> V:=simplify(V) ;

1

V \= ~m g x(/) + kS_st + x(f) + — k x(ć)

> V:-subs(delta[st3 = (m*g)/k,v);

V:=hx(tf

>zasada zachowania energii:-E+V=0;

1    (d    1 „(d

zasada zachowania energii: = — m — x(n H—Af — x(n

2    1,0/ ^WJ 4 [di

+ —kx(t)² = 0 2

>diff(zasada zachowania energii,t);

^Hl^x(0 K^x(,)

⁺Mf^x(/)

f d^2 ^
	+ £x(/)	9?|< !! O

>eqii:=siinplify(di£f (zasada zachowania energii, t) /diff (x(t) , t),symbolic);

+ -M 2

^5-x(/)| + *x(0 = 0

> equl:=collect(egu,< equl :=	di££(x(t] f 1 m + — 2 J	fs^2 ,0 xr^x« 9		2))); 4- £x(/) = 0
>egu4:=dsolve(egul,x(t)) ; , ^ „, • f 'FŻyfkt ' egu4x(t)); = Cl sin . ^V2m + A/ ^			+ C2cos		diTkt ^ ^^2m + M j

>_Cl:=di££(x[0] (t) , t) / (k/ (m+l/2*M)) ; C2:=0;

3    i

1

Cl

^x₀(0 || m +

k

C2:= 0

> egu 4;

|sin

k

4l4kt

yjlm+M

*(0 =