This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Displacement in SHM x = A ( t) where = sqrt((k)/(m)). Step 2: Velocity v = (dx)/(dt) = -A ( t). Step 3: Kinetic energy K = (1)/(2) m v^2 = (1)/(2) m (A ( t))^2 = (1)/(2) m ^2 A^2 ^2( t). Step 4: Substitute ^2 = (k)/(m) K = (1)/(2) m ((k)/(m)) A^2 ^2( t) = (1)/(2) k A^2 ^2( t). Step 5: Potential energy U = (1)/(2) k x^2 = (1)/(2) k (A ( t))^2 = (1)/(2) k A^2 ^2( t). Step 6: Total energy E = K + U = (1)/(2) k A^2 ^2( t) + (1)/(2) k A^2 ^2( t) = (1)/(2) k A^2 (^2( t) + ^2( t)). Step 7: Simplify using trig identity ^2 + ^2 = 1 E = (1)/(2) k A^2. Step 8: Proportionality E k and E A^2. E does not depend on m, and is not proportional to A. Final answer: (2) and (4)