A block of mass m is attached to a light spring of force constant k and executes simple harmonic motion with a time period T . If a graph is plotted with T on the y -axis and m on the x -axis, the slope of the resulting straight line is:

Step-by-step solution

The time period T of a spring-mass system is given by: T = 2 m k Taking the logarithm on both sides, we get: T = ( 2 ( m k )^ 1 2 ) T = 1 2 m + ( 2 k ) Comparing this with the equation of a straight line, y = mx + c , where y = T and x = m , the slope of the line is the coefficient of m . Therefore, the slope is 1 2 . Answer: 1 2