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Find T_b-T_T, the difference between the tension in the string at the bottom relative to that at the top of the circle.

Express the difference in tension in terms of m and g

The tension in the bottom i got was

T_b=v_b^2/L*m+(m*g)

the tension in the top i got was

T_t=m(-v_t^2/L)-m*g

to relate these and the total mech i did

v_t^2 =v_b^2-4*g*L

and i solved and i got 4*m*g and it marked it wrong saying "Check the energy difference between top and bottom in your calculation." can anyone help?