Solve the equations for v x </msub> and v y </msub> :

kwisangqaquqw3 2022-05-10 Answered
Solve the equations for v x and v y :
m d ( v x ) d t = q v y B m d ( v y ) d t = q v x B
by differentiating them with respect to time to obtain two equations of the form:
d 2 u d t 2 + α 2 u = 0
where u = v x or v y and α 2 = q B / m. Then show that u = C cos α t and u = D sin α t , where C and D are constants, satisfy this equation
Whenever I differentiate the first equation with respect to time, I get a resulting equation with the form:
d 2 u d t 2 + α 2 d u d t = 0
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Answers (1)

cegielnikmzjkf
Answered 2022-05-11 Author has 14 answers
Differentiating the first equation -
m v ¨ x = q v ˙ y B m v ¨ x = q 2 B 2 m v x v ¨ x + ( q B m ) 2 v x = 0
Where I have substituted for v ˙ y from equation 2.
You will get a similar equation on differentiation equation 2 for v ¨ y . And then of course given α = q B m you can get solutions as -
u = A cos ( α t ) + B sin ( α t ) u = v x , v y
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