The time period of a particle in simple harmonic motion is equal ,

(a) As x increases k increases.  Explanation: Since the motion is simple harmonic, the force F=-⍵²x where ⍵² is a constant. Equating the force applied by the student we get, -k/x=-⍵²x  →k=⍵²x²  It is...

(b) an extreme position  EXPLANATION:  At the extreme position the particle is in the same phase at consecutive appearance, hence (b) is true. In all other options, the consecutive appearance of the...

The correct answer is (d) zero. EXPLANATION:   The displacement is a vector and its magnitude is given by the line joining the initial position to the final position. Since after one time period...

The correct answer is (d) zero. EXPLANATION:   Since the acceleration is proportional to the displacement and always directed towards the mean position, half of one time period it is directed towards left and...

The correct answer is (b) B EXPLANATION: The equation can be written as x-A=B.sin⍵t If x-A=y then y=B.sin⍵t This is the equation of a simple harmonic motion with amplitude B. Hence option(b). 

(a) 1/2 m ω2 A2   EXPLANATION:   The total energy at any instant in a simple harmonic motion is constant and equal to ½m⍵²A². Hence the average energy in one time period will also...

The correct answer is (c) 2 v EXPLANATION:  Between one extreme position to another i.e. in half the time period the K.E. increases from zero to maximum (at the mean position) and again...

(d) become T/√2. EXPLANATION:   The time period of a spring-mass system is given as T = 2π√(m/k).  When the spring is divided in two equal halves the spring constant of each half doubles,...

(a) displacement from the mean position EXPLANATION:   Since a=-⍵²x, where x is the shortest instantaneous distance from the mean position i.e. magnitude of the displacement from the mean position. Hence (a) is...

(a) 1/2 m ω2 A2   EXPLANATION:   The total energy at any instant in a simple harmonic motion is constant and equal to ½m⍵²A². Hence the average energy in one time period will also be...