Question

A mass attached to a spring executes SHM

Match the following conditions.

(i) $v_x>0,a_x>0\left(I\right)x>0$

(ii) $v_x<0,a_x>0$

(iii) $v_x>0,a_x<0\left(II\right)x<0$

(iv) $v_x<0,a_x<0$

• A. (i) - II; (ii) - I; (iii) - I; (iv) - I
• B. (i) - II; (ii) - II; (iii) - I; (iv) - I
• C. (i) - I; (ii) - II; (iii) - I; (iv) - I
• D. (i) - I; (ii) - I; (iii) - II; (iv) - II

Answer 1

The correct option is B

(i) - II; (ii) - II; (iii) - I; (iv) - I

One thing we know about SHM is that the force (F$\propto$ - x) in case of a simple spring this becomes F = -kx as we also know that F = ma. We can get $a\propto -x$. let's make an observation of sign of a and x. when x $>$ 0, we get a $<$0 and when x $<$ 0 we get a $>$ 0. So whenever acceleration is negative the position is positive and vice versa. We don't even need to know the direction of velocity for that! So very simply if we analyze the options only (b) would be the correct one.