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एक पिंड सरल आवर्त गति करता है जिसकी आवृत्ति, , प्रारंभिक विस्थापन
तथा प्रारंभिक वेग
है। पिंड के दोलन का आयाम, अधिकतम वेग तथा अधिकतम त्वरण परिकलित करें।
क) तीन सदिश ,
और
प्रतिबंध
को संतुष्ट करते हैं। यदि
और
तो
का मान ज्ञात करें।
Three vectors ,
and
satisfy the condition
. If
and
determine the value of
.
A block of mass is moved up from the base a rough inclined plane making an angle of
with the horizontal with initial speed
. The coefficient of kinetic friction between the block and the plane is 0.2. Calculate
i) the maximum distance the block travels up the incline before coming to rest.
ii) the speed of the block when it returns to the base of the inclined plane.
iii) the energy lost over the entire motion. Take .
Two collinear harmonic oscillations, each of frequency , have amplitudes, a1 and a2 and initial phases,
and
, respectively. Show that, when these oscillations are superposed, the amplitude of the resultant motion is equal to (a1 - a2). What will be the value of the resultant amplitude when
and
.
Given that the time period of Halley's comet is , calculate the length of its semi-major axis. If the perihelion distance of the orbit is
, calculate the aphelion distance.