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 Bby differentiating them with respect to time to obtain two equations of the form: d 2 u d t 2 + α 2 u = 0where 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 equationWhenever 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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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    Bby differentiating them with respect to time to obtain two equations of the form:                    d        2            u              d              t        2              +      α    2    u  =  0where   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 equationWhenever 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

cegielnikmzjkf · Accepted Answer

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    =  0Where 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

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

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