If x = a cos nt – b sin nt, then \(\frac{d^2x}{dt^2}\) is A. n2x

1.	If x = a cos nt – b sin nt, then \(\frac{d^2x}{dt^2}\) is A. n2x B. –n2x C. –nx D. nx
Answer» Correct Answer is (B) - n² x Given: x=a cos nt-b sin nt \(\frac{dx}{dt}\)\(\)= -an sin nt - bn cos nt \(\frac{d^2x}{dt^2}\)= -an²cos nt + bn² sin nt = -n² (a cos nt-b sin nt ) = - n² x

If x = a cos nt – b sin nt, then \(\frac{d^2x}{dt^2}\) is A. n2x B. –n2x C. –nx D. nx

Answer»

Correct Answer is (B) - n² x

Given:

x=a cos nt-b sin nt

\(\frac{dx}{dt}\)\(\)= -an sin nt - bn cos nt

\(\frac{d^2x}{dt^2}\)= -an²cos nt + bn² sin nt

= -n² (a cos nt-b sin nt )

= - n² x