QAIPM-2002-Ph-2821: NEET 2002 Physics - Class 11 AIPM-2002-Ph-2821 Solution: A mass is suspended separately by two different springs in…

The time period of a spring mass system as shown in figure 1 is given by T = 2 � m / k , where k is the spring constant. _ t 1 = 2 � m / k 1    ...(i) and t 2 = 2 � m / k 2    ...(ii) Now, when they are connected in parallel as shown in figure 2(a), the system can be replaced by a single spring of spring constant, k eff = k 1 + k 2 . [Since mg = k 1 x + k 2 x = k eff x] _ t 0 = 2 � m / k e f f = 2 � m / ( k 1 + k 2 )    ...(iii) From (i), 1 t 1 2 = 1 4 � 2 _ k 1 m    ...(iv) From (ii), 1 t 2 2 = 1 4 � 2 _ k 2 m    ...(v) From (ii), 1 t 0 2 = 1 4 � 2 _ k 1 + k 2 m    ...(vi) Now (iv) + (v) 1 t 1 2 + 1 t 2 2 = 1 4 � 2 m ( k 1 + k 2 ) = 1 t 0 2 _ t 0 _ 2 = t 1 _ 2 + t 2 _ 2