A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is (a) at the end A, (b) at the end B, (c) at the mid-point of AB going towards A, (d) at 2 cm away from B going towards A, (e) at 3 cm away from A going towards B, and (f) at 4 cm away from B going towards A.
Given: A particle is in SHM between two point A and B. The distance between A and B is 10 cm .
The direction from A to B is positive.
(a)
The figure below shows two end points A and B with their mid-pint as O.
If the particle is in SHM between the points A and B then at extreme points A and B the particle is at rest. The velocities at extreme points are zero.
At point A, the particle tends to move towards O to remain continue in motion. Thus, the direction of acceleration is pointed towards O. The direction along AB is positive. The acceleration is positive and directed along AO. Force is also positive as the acceleration is in positive direction.
Thus, the velocity at extreme point A is zero. The acceleration and force are positive.
(b)
The figure below shows two end points A and B with their mid-pint as O.
If the particle is in SHM between the points A and B then at extreme points A and B the particle is at rest. The velocities at extreme points are zero.
At point B, the particle tends to move towards O to remain continue in motion. Thus, the direction of acceleration is pointed towards O. The direction along AB is positive. The acceleration is negative and directed along BO. Force is also negative as the acceleration is in negative direction.
Thus, the velocity at extreme point B is zero. The acceleration and force are negative.
(c)
The figure below shows two end points A and B with their mid-pint as O.
The particle is in SHM. At point O the particle is at its mean position. The velocity at this point is maximum. The particle is moving towards B, the direction of velocity is in negative direction.
The net force at its mean position is zero. So the acceleration is also zero at its mean position.
Thus, the velocity at point O is maximum. The acceleration and force are zero.
(d)
The given figure has shown below shows two end points A and B with their mid-pint as O.
The particle is moving towards O from point B. the direction of motion is opposite to the conventional positive direction from A to B.
Thus, the particle velocity, acceleration and force all are negative.
(e)
The given figure has shown below shows two end points A and B with their mid-pint as O.
The particle is moving towards O from point A. The direction of motion is to the positive direction from A to B.
Thus, the particle velocity, acceleration and force all are positive.
(f)
The given figure has shown below shows two end points A and B with their mid-pint as O.
The particle is moving towards O from point B. the direction of motion is opposite to the conventional positive direction from A to B.
Thus, the particle velocity, acceleration and force all are negative.
Given: A particle is in SHM between two point A and B. The distance between A and B is
The direction from A to B is positive.
(a)
The figure below shows two end points A and B with their mid-pint as O.
If the particle is in SHM between the points A and B then at extreme points A and B the particle is at rest. The velocities at extreme points are zero.
At point A, the particle tends to move towards O to remain continue in motion. Thus, the direction of acceleration is pointed towards O. The direction along AB is positive. The acceleration is positive and directed along AO. Force is also positive as the acceleration is in positive direction.
Thus, the velocity at extreme point A is zero. The acceleration and force are positive.
(b)
The figure below shows two end points A and B with their mid-pint as O.
If the particle is in SHM between the points A and B then at extreme points A and B the particle is at rest. The velocities at extreme points are zero.
At point B, the particle tends to move towards O to remain continue in motion. Thus, the direction of acceleration is pointed towards O. The direction along AB is positive. The acceleration is negative and directed along BO. Force is also negative as the acceleration is in negative direction.
Thus, the velocity at extreme point B is zero. The acceleration and force are negative.
(c)
The figure below shows two end points A and B with their mid-pint as O.
The particle is in SHM. At point O the particle is at its mean position. The velocity at this point is maximum. The particle is moving towards B, the direction of velocity is in negative direction.
The net force at its mean position is zero. So the acceleration is also zero at its mean position.
Thus, the velocity at point O is maximum. The acceleration and force are zero.
(d)
The given figure has shown below shows two end points A and B with their mid-pint as O.
The particle is moving towards O from point B. the direction of motion is opposite to the conventional positive direction from A to B.
Thus, the particle velocity, acceleration and force all are negative.
(e)
The given figure has shown below shows two end points A and B with their mid-pint as O.
The particle is moving towards O from point A. The direction of motion is to the positive direction from A to B.
Thus, the particle velocity, acceleration and force all are positive.
(f)
The given figure has shown below shows two end points A and B with their mid-pint as O.
The particle is moving towards O from point B. the direction of motion is opposite to the conventional positive direction from A to B.
Thus, the particle velocity, acceleration and force all are negative.
