A simple harmonic oscillator has amplitude 15 cm and it completes 100 oscillations in 50 s. (i) Calculate its time period and angular frequency. (ii) If the initial phase is
π/2, write expressions for its displacement and velocity. (iii) Calculate the values of maximum velocity and acceleration.
We are given: * Amplitude $A = 15\, \text{cm} = 0.15\, \text{m}$ * Number of oscillations $= 100$ * Time taken $= 50\, \text{s}$ * Initial phase $\phi = \frac{\pi}{2}$ --- ### (i) Time period and angular frequency Time period $T$ is the time for one oscillation: $$ T = \frac{\text{Total time}}{\text{Number of oscillations}} = ________ _____ _________ __________ _________.
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A box of mass 10 kg is being pulled on the floor by a mass-less rope with a force of 100 N at an angle of 60o to the horizontal. What is the acceleration of the box if the coefficient of kinetic friction between the floor and the box is µε -0.257 Take g-10 ms.-2
बृहस्पति की दीर्घवृत्तीय कक्षा के लिए e= 0.05 है और अर्ध-दीर्घ अक्ष 7.8×10-¹¹m है। ग्रह की ऊर्जा तथा रविनीच और रविउच्च बिंदुओं की दूरियां ज्ञात करें।
के लिए।
A small satellite is in a circular orbit around a planet at a distance of 4.0 x 108 m from the centre of the planet. The orbital speed of the satellite is 200 ms. What is the mass of the planet?
एक सरल आवर्त दोलक का आयाम 15 cm है और यह 50s में 100 दोलन पूरे करता है। (i) इस दोलक का आवर्तकाल और कोणीय आवृत्ति परिकलित करें। (ii) यदि इस दोलक की प्रारंभिक कला /2 है तो इसके विस्थापन और वेग के लिए व्यंजक लिखें। (iii) इसके वेग तथा त्वरण का अधिकतम मान परिकलित करें।
A block of mass 5.0 kg starts from rest and slides down a surface which corresponds to a quarter of a circle of 3.0 m radius. (i) If the curved surface is smooth, find the speed at the bottom. (ii) If the speed at the bottom is 2.0 ms", calculate the energy dissipated due to friction in the descent. (iii) After the block reaches the horizontal with a speed of 2.0 msit slides to a stop in a distance of 1.5 m. calculate the frictional force acting on the horizontal surface. Take g-10ms-2.
Determine the torque about the point (0, 1, 1) due to a force being exerted at the point (4, 2, 3).