{"id":260546,"date":"2022-09-10T12:27:56","date_gmt":"2022-09-10T06:57:56","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-particle-is-performing-simple-harmonic-motion-along-x-axis-with-amplitude-4-cm-and-time-period-1-2-s-the-minimum-time-taken-by-the-particle-to-move-from-x2cm-to-x4and-back\/"},"modified":"2022-09-10T12:27:56","modified_gmt":"2022-09-10T06:57:56","slug":"a-particle-is-performing-simple-harmonic-motion-along-x-axis-with-amplitude-4-cm-and-time-period-1-2-s-the-minimum-time-taken-by-the-particle-to-move-from-x2cm-to-x4and-back","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-is-performing-simple-harmonic-motion-along-x-axis\/","title":{"rendered":"\u00a0A particle is performing simple harmonic motion along x-axis with amplitude 4 cm and time period 1.2 s. The minimum time taken by the-particle to move from\u00a0x=+2cm\u00a0to\u00a0x=+4and back again is given by\u00a0\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"\u00a0A particle is performing simple harmonic motion along x-axis with amplitude 4 cm and time period 1.2 s. The minimum time taken by the-particle to move from\u00a0x=+2cm\u00a0to\u00a0x=+4and back again is given by\u00a0\u00a0","custom_permalink":"question\/physics\/a-particle-is-performing-simple-harmonic-motion-along-x-axis\/"},"categories":[],"acf":{"question":"

 A particle is performing simple harmonic motion along x-axis with amplitude 4 cm and time period 1.2 s. The minimum time taken by the-particle to move from x<\/mi>=<\/mo>+<\/mo>2<\/mn>cm<\/mi> to <\/mtext>x<\/mi>=<\/mo>+<\/mo>4<\/mn><\/math>and back again is given by 
 <\/p>","options":[{"option":"

0.6 sec<\/p>","correct":false},{"option":"

0.4 sec<\/p>","correct":false},{"option":"

0.3 sec<\/p>","correct":true},{"option":"

0.2 sec<\/p>","correct":false}],"solution":"

short cut : t = 2<\/mn>T<\/mi><\/mrow>6<\/mn><\/mfrac>=<\/mo>T<\/mi>3<\/mn><\/mfrac><\/math>=0.4 sec
 <\/p>
<\/figure>

Time taken from O to A
=<\/mo>T<\/mi>8<\/mn><\/mfrac>=<\/mo>1<\/mn>\u22c5<\/mo>2<\/mn><\/mrow>8<\/mn><\/mfrac>=<\/mo>0<\/mn>\u22c5<\/mo>3<\/mn><\/mrow>2<\/mn><\/mfrac> <\/mspace>Time<\/mi> <\/mo>taken<\/mi> <\/mo>from<\/mi> <\/mo>O<\/mi> <\/mo>to<\/mi> <\/mo>B<\/mi>.<\/mo> <\/mspace>=<\/mo>T<\/mi>4<\/mn><\/mfrac>=<\/mo>1<\/mn>\u22c5<\/mo>2<\/mn><\/mrow>4<\/mn><\/mfrac>=<\/mo>0<\/mn>\u22c5<\/mo>3<\/mn> <\/mspace>Tlme<\/mi> <\/mo>taken<\/mi> <\/mo>from<\/mi> <\/mo>A<\/mi> <\/mo>to<\/mi> <\/mo>B<\/mi> <\/mspace>=<\/mo>0<\/mn>\u22c5<\/mo>3<\/mn>\u2212<\/mo>0<\/mn>\u22c5<\/mo>3<\/mn><\/mrow>2<\/mn><\/mfrac><\/mrow><\/mfenced>=<\/mo>0<\/mn>\u22c5<\/mo>3<\/mn><\/mrow>2<\/mn><\/mfrac> <\/mspace> Total time taken <\/mtext>=<\/mo>2<\/mn>\u00d7<\/mo>0<\/mn>\u22c5<\/mo>3<\/mn><\/mrow>2<\/mn><\/mfrac>=<\/mo>0<\/mn>\u22c5<\/mo>3<\/mn>sec<\/mi><\/math><\/p>","subject":""},"yoast_head":"\n\u00a0A particle is performing simple harmonic motion along x-axis with amplitude 4 cm and time period 1.2 s. 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