...the velocity destroyed varies as the space described. 6. A particle slides down the smooth arc of a cycloid, whose axis is vertical, and vertex downwards, to find the time of an oscillation. Let AB be the vertical axis of the cycloidal arc APL, L the point from which the particle...

...the velocity destroyed varies as the space described. 6. A particle slides down the smooth arc of a cycloid, whose axis is vertical, and vertex downwards, to find the time of an oscillation. Let AB be the vertical axis of the cycloidal arc APL, L the point from which the particle...

...depths of its ends below a fixed horizontal straight line. 1443. A uniform heavy string is placed on the arc of a smooth cycloid, whose axis is vertical and vertex upwards; determine the motion, and prove that, so long as the string is wholly in contact with the...

...since the circle turns through 2<7 two right angles, while the tracing point passes from A to 0. 147. A particle starts from rest at any point in the arc...the point from which the particle starts. Through Tdraw TC parallel to AD, and let a second cycloid OA' be drawn, having its vertex at O and O0 for axis....

...will be in relative equilibrium in the tube. 1.9. Shew that if a heavy particle fall from a cusp down the arc of a smooth cycloid whose axis is vertical and vertex downwards, its pressure on the curve at its lowest point will be equal to twice its weight. 20. Supposing the...

...divide the arc between two cusps in the ratio 2n — 1 : 2n + I. 2f>79. A heavy particle falls down the arc of a smooth cycloid whose axis is vertical and vertex upwards in a medium whose resistance is mass x (velocity )*-=-2e, its distance along the arc from the...

..., since the circle turns through two right angles, while the tracing point passes from A to O. 220. A particle starts from rest at any point in the arc...second cycloid OA' be drawn, having its vertex at O and O0 for axis. Let OD be denoted by a, OC by a. Let Q be any point on the first cycloid between T and...

...other end being initially at C, when it is unwrapped the free end will describe the cycloid CAC'. 166. A particle starts from rest at any point in the arc...cycloid whose axis is vertical and vertex downwards; to dismiss the motion. Let CAC' be the cycloid, C, C' the cusps, A the vertex, AB perpendicular to CC'...

...other end being initially at C, when it is unwrapped the free end will describe the cycloid CAC'. 166. A particle starts from rest at any point in the arc...cycloid whose axis is vertical and vertex downwards ; to discuss ihe motion. Let CAC' be the cycloid, C, C' the cusps, A the vertex, AB perpendicular to CC'...

...similar, Pis a point in the cycloid whose axis is AB. 109. A particle slides down the smooth arc of a cycloid, whose axis is vertical, and vertex downwards, to find the time of an oscillation. Let AB be the vertical axis of the cycloidal arc APL, L the point from \\ bich the...