May Anyone answer the question from 1 to 10. 2T 1. A mass m hanging on a spring
ID: 249852 • Letter: M
Question
May Anyone answer the question from 1 to 10.2T 1. A mass m hanging on a spring has simple harmonic motion with a period T. If a mass 3m is hung from the same spring the period of oscillations is (a) T b) T/3 (d) BT e)3T 13 2. If a body is moving with simple harmonic motion then the force that is being acted on the body is (a) constant b) proportional to the sine or cosine function of displacement. (c) proportional to the inverse square of the displacement (d) directly proportional to the displacement. (e) proportional to the square of the displacement. constant k The block sits on a hoeizontal n the mass is pulled a distance A from Questions 3 and 4 A block of mass M is attached to a speing of frictionless table with one end of the spring attached to a fixed point. equilibrium and released, it oscillates with a period of T and the total energy of the spring-block system is E Assume small displacements in the oscillations such that the motion is simple harmonic. Now the block is pulled a distance 2A and released from rest 3. If the new period of oscillations is T, then (a) T-47 (d) 7-1 b) T-27 (e) (c) T-T (f) none of the above 4 If the new total energy of the system is E, then (a) E-2E (d) E-E (c) E- (f) none of the above b) E-4E 5. Consider a block of mass m attached to a vertical spring with spring constant k. When on earth, for small oscillations the period of the system is T. Now it is taken to a planet where the acceleration due to gravity is g/2 If the new period is Ti then (a) Ti=T (c) T. = T/2 6. A simple pendulum consists of mass M attached to a string of length L It is at a location where the is T. Now the bob of the acceleration due to pendulum is replaced with a new bob of mass 2M. If the new period is T. then is g The of small oscillations of the (a) Ti b) T 21 ) T-T2 T-4T 7. A simple pendulum consists of mass M attached to a string of length L. It is at a location where the is T.Now the string od the acceleration due to gravity is g The period of small oscillations of the pendulum is replaced with a new string of length 2L If the new period is T. then (a) Ti-T ) T-T2 T-4T Questions 8-9 A small plate (black) of mass M is attached to a spring of spring constant. When it is at location B, the spring is completely relaxed
Explanation / Answer
1)
you need to use:
T = 2*pi*sqrt (m/K)
T is directlu proportional to sqrt (m)
Tf/Ti = sqrt (mf/mi)
Tf/T = sqrt (3m /m)
Tf/T = sqrt (3)
Tf= T* sqrt (3)
Answer: d
2)
for simple harmonic equation,
F = -K*x
So force is directly proportional to displacement
Answer: d
3)
T = 2*pi*sqrt (m/K)
It doesn't depend on amplitude
So period will not change
Hence T1=T
Answer: C
4)
Total energy = 0.5*K*A^2
Total energy is proportional to amplitude A^2
so,
E1/E = (2A)^2/ (A)^2
E1/E = 4* A^2/ A^2
E1/E = 4
E1 = 4*E
Answer: B
I am allowed to answer only 4 subparts at a time
I have answered 1st 4 for you
Thanks